EQUINE IMMOBILIZATION WITH A LIMB RESTRAINT SYSTEM

Transcription

1 EQUINE IMMOBILIZATION WITH A LIMB RESTRAINT SYSTEM A Thesis Submitted to the Coege of Graduate Studies and Research In Partia ufiment of the Requirements or the Degree of Master of Science In the Department of Mechanica Engineering University of Saskatchewan Saskatoon By Wei Cai Keywords: Standing Horse, Mobiity, Joint Restraints, Breaking orce, Immobiization, Copyright Wei Cai, June, 007. A rights reserved.

2 PERMISSION TO USE In presenting this thesis in partia fufiment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freey avaiabe for inspection. I further agree that permission for copying of this thesis in any manner, in whoe or in part, for schoary purposes may be granted by the professor or professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the Coege in which my thesis work was done. It is understood that any copying or pubication or use of this thesis or parts thereof for financia gain sha not be aowed without my written permission. It is aso understood that due recognition sha be given to me and to the University of Saskatchewan in any schoary use which may be made of any materia in my thesis. Requests for permission to copy or to make other use of materia in this thesis in whoe or part shoud be addressed to: Head of the Department of Mechanica Engineering University of Saskatchewan Saskatoon, Saskatchewan S7N 5A9

3 ABSTRACT Mobiity of the horse to initiate motion from the standing position is examined in this thesis. In particuar, the thesis focuses on the study of the mobiity of a horse with fixed hooves to the ground, and on how its muscuoskeeta system is used to free the egs from restraints. Possibe eg patterns to initiate motions are investigated. The breaking forces generated at front and hind hooves during static-puing and dynamic jerking are evauated. Design of the restraint system that uses ropes to immobiize certain joints in order to prevent the horse from generating these forces is the main objective of this thesis. Such a system coud be appied as an aternative to rather massive mechanica devices, the main purpose of which is to bock the breaking forces (which are quite arge when fuy deveoped). Anaysis of the mobiity of the horse is based on the mechanics of a skeeta inkage system driven by musce forces. Ony major musces invoved in fighting the restraints are incuded in the anaysis. The force generation capabiity of a musce is determined by physioogica cross sectiona area (PCSA) of the musce. Possibe eg patterns are predicted with the kinematics anaysis considering range of motion at each joint in the egs. Corresponding breaking forces generated in each pattern is evauated with the kinetics anaysis. Reationship between the characteristic parameter of the pattern and the breaking force at hoof are estabished. The horse's computer mode is used to justify the anaytica resut. ighting mechanisms of the horse are simuated in the dynamic simuation software package. Patterns and the breaking forces deveoped by the horse mode simuation agree we with the anaytica resuts. To the iii

4 author s best knowedge, this is the first time a computer mode is used in anayzing the method of restraining an anima. The mobiity of the anima with hoof restraints and methods to remove mobiity were further confirmed with a preiminary anima restraint test conducted on a sheep. The sheep was chosen because the eg patterns to initiate motion on a horse are simiar to that of sheep, but the sheep is more convenient to hande. The experiment showed that the mobiity of the sheep coud be removed competey by restraining its hooves, ower egs, and head with easiy attached ropes. iv

5 ACKNOWLEDGMENTS This thesis cannot be accompished if not for the hep from many peope and their support. I woud ike to take this opportunity to thank my supervisor Professor Waerian Szyszkowski, PhD, PEng, who guided me through the research with his enthusiasm, understanding and invauabe knowedge. My appreciation aso goes to my committee members Prof. Gregg Adams, Prof. Dean Chapman and Prof. Richard Burton for their vauabe suggestions and continuing encouragement. Specia thanks to Prof. Gen Watson for his support over the years. The contributions of Prof. Peter ood, Prof. Ronad Chapin from the Western Coege of Veterinary Medicine and Mr. Hans Steinmetz from the Department of Mechanica Engineering in setting up the experiments and sharing of their expertise are truy appreciated. During the course of this work, I was supported by NSERC and SSI grant through Prof. Gen Watson, Prof. Waerian Szyszkowski and Prof. Gregg Adams. Sincere appreciation aso goes to my husband Goh Wee Seng, parents Cai uhe, An Ping and sister Cai Jin for their ove and support. v

6 DEDICATION This thesis is dedicated to the author s parents Cai, uhe & An, Ping

7 TABLE O CONTENTS PERMISSION TO USE... ii ABSTRACT... iii ACKNOWLEDGMENTS...v DEDICATION... vi LIST O TABLES... xi LIST O IGURES... xii LIST O ABBREVIATION...xv. INTRODUCTION.... Immobiizing a Horse.... Mechanism of Initiating Motion with ixed Hooves and the Method of Anaysis The Muscuoskeeta System of a Horse Mechanics of the Limb Linkage System Computer Mode of the Horse...7. ORELIMB RETRAINT METHOD...9. oreimb Muscuoskeeta Structure and Mobiity...9. Mechanica Mode of the Horse oreimb in the Standing Configuration..... The oreimb Mechanica Mode..... The oreimb Anatomica Computer Mode Kinematics of the oreimb Mechanica Mode... 6 vii

8 ..4 The oreimb Quasi-Static Puing The Breaking orce Due to oreimb Dynamic Jerking oreimb Jerking by Lowering the Body ( Down Maneuver ) oreimb Jerking by Eevating the Body (Up Maneuver) REMOVING THE ORELIMB MOBILITY Effect of Adding Additiona Restraints orces in the Additiona Restraints HINDLIMB RESTRAINT METHOD Hindimb Muscuoskeeta Structure and Mobiity Mechanica Mode of the Hindimb in the Standing Configuration The Hindimb Mechanica Mode The Hindimb Anatomic Computer Mode The Hindimb Quasi-Static Puing The Breaking orce Due to Hindimb Dynamic Jerking Hindimb Jerking By Lowering the Hip (Down Maneuver) Hindimb Jerking by Eevating the Hip (Up Maneuver) REMOVING THE HINDLIMB MOBILITY Effect of Adding Hock Joint Restraint in Natura Standing and Stretching Configurations Required Restraint orce at Hock Joint THE SHEEP RESTRAINING EXPERIMENT Appying Initia Restraints Sheep Cart Hoof Restraint viii

9 6..3 Head Restraint Mobiity of the Initiay Restrained Sheep oreimb Mobiity Quasi-Static Puing oreimb Mobiity Dynamic Jerking Hindimb Mobiity Quasi - Static Puing Hindimb Mobiity Dynamic Jerking Adding the Hock Restraint to Immobiize the Hindimb Restraining the Sheep in the Legs Spread Position CONCLUSION AND UTURE WORK...83 LIST O REERENCES...87 APPENDIX A. EVALUATION O LIMB MUSCLE ORCES IN IGHTING THE RESTRAINTS...89 A. oreimb Musces...89 A. Hindimb Musces...9 APPENDIX B. GENERATING THE HORSE MODEL IN SOLIDWORKS...93 B. Defining the Geometric Shape of the Horse...93 B. Physica Properties of Body Segment...95 APPENDIX C. MOTION SIMULATION...96 C. Adding Constraints in the Mode...96 C.. Joint Constraint C.. Hoof Constraint C..3 Upper Arm and Trunk Constraint C..4 Lower Leg Restraint ix

10 C. Appying Musce orce...98 C.3 Initia Veocity and Acceeration...99 C.4 Body Resistance to Motion...99 APPENDIX D. MIXED DIERENTIAL ALGEBRAIC EQUATION O MOTION...0 x

11 LIST O TABLES Tabe Page Tabe : Horse Body Segment Properties...94 xi

12 LIST O IGURES igure page igure.: Weight shifting mechanism to free the foreimb...4 igure.: Scheme of anayzing restraint method...5 igure.: Skeeton of the horse foreimb...0 igure.: Linkage system of the horse foreimb and the ROM at each joint... igure.3: Mechanica mode of the foreimb...4 igure.4: Computer mode of the horse foreimb...5 igure.5: Geometric configuration of the foreimb...7 igure.6: Joint anges versus vertica dispacement of the foreimb...9 igure.7: orce diagram of the foreimb in static puing... igure.8: oreimb hoof s breaking force versus vertica dispacement of joint A...3 igure.9: Joint reaction force versus vertica dispacement of joint A...3 Ax igure.0: Anaysis of the foreimb static puing approaching to the top...4 igure.: Breaking force in static puing...5 igure.: oreimb in dynamic jerking...7 igure.3: Ebow (joint A) motion in dynamic jerking (down maneuver)...8 igure.4: oreimb force diagram in dynamic jerking ()...3 igure.5: oreimb force diagram in dynamic jerking ()...34 igure.6: oreimb simuation modes...35 igure.7: oreimb mode incuding the horse trunk...36 igure.8: The forces due to foreimb dynamic jerking (down maneuver)...38 igure.9: Ebow joint (joint A) motion in dynamic jerking (up maneuver)...40 igure.0: Breaking force due to foreimb dynamic jerking (up maneuver)...4 xii

13 igure 3.: Additiona restraining of the foreimb's DOs...4 igure 3.: orce diagram of the foreimb with carpa, fetock and hoof restraints...45 igure 3.3: Modes of restrained foreimb used in the COSMOS simuations...46 igure 3.4: orces on the foreimb versus restraint attachment anges...48 igure 4.: Hindimb skeeta structure...5 igure 4.: Linkage system of hindimb and the ROM at each joint...5 igure 4.3: Mechanica mode of the horse hindimb...54 igure 4.4: Overview structure of the hindimb...55 igure 4.5: orce diagram of hindimb quasi-static puing...57 igure 4.6: Hindimb in dynamic jerking...59 igure 4.7: Stife joint (joint A) motion in dynamic jerking (down maneuver)...60 igure 4.8: orces due to hindimb dynamic jerking (down maneuver)...6 igure 4.9: Stife joint (joint A) motion in dynamic jerking (up maneuver)...63 igure 4.0: orces due to hindimb dynamic jerking (up maneuver)...64 igure 5.: Adding hock restraint on the hind imb in two configurations...66 igure 5.: orce diagram with hock restraint...68 igure 5.3: The COSMOS modes of hindimb with hock and hoof restraints...70 igure 5.4: Required hock reaction forces versus the restraint attachment ange...70 igure 5.5: Required breaking force versus restraint attachment ange...7 igure 6.: Sheep cart...73 igure 6.: Sheep fighting without hoof restraints...73 igure 6.3: Hoof restraints...74 igure 6.4: Sheep body movement without the head restraint...75 igure 6.5: Head restraint...75 igure 6.6: Overview of the sheep initia restraints...76 xiii

14 igure 6.7: Quasi-static puing on the sheep foreimb...77 igure 6.8: Dynamic jerking on the sheep foreimb...78 igure 6.9: Dynamic jerking on sheep hindimb...79 igure 6.0: Sheep restrained with hock restraints and hoof restraints...80 igure 6.: Sheep free itsef from improper hock restraint...80 igure 6.: Sheep restrained in egs spread position...8 igure 6.3: Sheep hindimb stretched to aign...8 igure 7.: Horse restraint patform...85 igure A.: Upper foreimb musce forces in foreimb...90 igure A.: Lower foreimb musce forces...90 igure A.3: Upper hindimb musce forces...9 igure A.4: Lower hindimb musce forces...9 igure B.: Twenty-six segment mode of a Dutch Warm Bood horse...93 igure B.: Creating 3D horse mode...94 igure C.: Modeing of hoof restraint...97 igure C.: Setting the transationa constraint at the upper arm...97 igure C.3: Setting the biceps musce force...98 igure C.4: Simuating body resistance to the motion...00 igure D.: DAE in matrix...05 xiv

15 LIST O ABBREVIATION A Ebow joint (f) or stife joint (h) a Acceeration a arm Moment arm of musce forces B Carpa joint (f) or hock joint (h) b Distance between ebow joint and biceps insertion point (f) or distance between stife joint and biceps femoris (h) B Breaking force at hoof C etock joint (f) or metatarsus joint (h) D Pastern and hoof joint E Shouder joint (f) or hip joint (h) e x Vertica distance between shouder joint and biceps insertion (f) or vertica distance between hip joint and biceps femoris insertion (h) in arbitrary pattern e y Horizonta distance between shouder joint and biceps insertion (f) or horizonta distance between hip joint and biceps femoris insertion (h) in arbitrary pattern 0 e x Vertica distance between shouder joint and biceps insertion (f) or vertica distance between hip joint and biceps femoris insertion (h) in rest standing pattern 0 e y Ax, Ay, A Bx, By or B br Cx, Cy or C Horizonta distance between shouder and biceps insertion (f) or horizonta distance between stife and biceps femoris insertion (h) in rest standing pattern Constraint force at carpa joint (f) or hock joint (h) Constraint force at fetock joint Reaction force at joint A Reaction force at joint B Breaking force at hoof Reaction force at joint C Dx, Dy Reaction force or breaking force at joint D m, p xi yi mx, my Biceps musce force orce to move the eg in vertica direction Externa force appied in x direction Externa force appied in y direction xv

16 H Length between ebow joint and hoof joint (f) or ength between stife joint and hoof joint (h) when the eg is stretched in a ine I Biceps (f) or Biceps femoris (h) insertion point i Number of part in the system J c Moment of inertia about centroid of ink J c Moment of inertia about centroid of ink j Number of coordinate k Number of constraint equations L Lagranian Length of ink Length of ink + ink3 ' Length of metacarpus (f) or metatartus (h) Length of pastern (f/h) ' 3 c Length between joint A and the center of mass of ink c Length between joint D and the center of mass of ink M Mass on top of foreimb or hindimb M i Moment appied on each part q Genera coordinates T Kinetic Energy of the system V Potentia Energy of the system x Dispacement of joint A x ci Dispacement of centroid of a part in x direction x stop Maximum dispacement of joint A before it stops v Veocity y ci Dispacement of the centriod of a part in y direction v max Maximum veocity of joint A before it stops α,β,γ Joint ange & α, & β, & γ Joint ange veocity & α, && β,& γ Joint ange acceeration Anguar dispacement λ Lagrange mutipier ϕ, ϕ Restraint attachment ange φ Constraint equations θ i k Note: f: foreimb h: hindimb xvi

17 . INTRODUCTION. Immobiizing a Horse Immobiizing a horse is often required for medica imaging procedures, transportation and veterinary medica examinations, etc. Based on the handing experience, some simpe restraint devices have been designed and used such as meta stocks, a tabe and straps, etc. Athough horses may generay be positioned as required, none of these devices removes the horse s mobiity sufficienty for imaging. Aso, such restraints aow the horses to strugge within them. As a consequence, the animas very frequenty injure themseves when fighting to break free and\or threatens the safety of handers. The other possibiity to immobiize a horse is to use genera anesthesia that wi competey parayze its musces. However a support breathing system is aways needed during genera anesthesia. In addition, specia treatment assisting the horse during recovery from genera anesthesia, such as a cushioned room or water poo, are typicay required to decrease the incidence and/or severity of post anesthetic compications. A of the compexity of administering genera anesthesia can be avoided if a mechanica device can competey eiminate the anima s mobiity, which is the object of this thesis. The novety of such a design wi be that instead of using mechanica devices to bock arge forces generated by a horse s musce, this design wi prevent the horse from generating such forces at a or wi reduce them substantiay. Therefore, this thesis focuses on mobiity of the horse and designing the restraint system to

18 remove it. A thorough understanding of the horse s mobiity is required for a successfu design of such a system. There is a perception that horses are designed by nature to run. Therefore, amost a research on the equine ocomotion system focused on the study of the anima in motion. There are many studies anayzing waking, running or jumping horses [,, 3, and 4]. Resuts from such studies do not hep in the design of a restraint method since none of them examines how the anima initiates motion from standing. Mobiity of the horse to initiate motion from the standing position is essentiay a new concept introduced in this thesis. In particuar, the thesis wi focus on the study of a horse with removed mobiity of the hoof. This is impemented by fixing horse hooves to the ground. The horse s body shoud remain motioness when mobiity of the egs is removed by means of restraints. Study of the mobiity of the horse is based on understanding the muscuoskeeta structure and the musce functions of the horse. The skeeta system was considered as a simpified mechanica inkage system. Prediction of possibe patterns of the initiation of motion was made by studying the inkage kinematics and dynamics. Methods to remove mobiity with externa restraints were deveoped based on anaytica cacuations, computer simuations and experimenta observations. Due to the cost and safety invoved, preiminary tests were preformed on sheep, which react somewhat simiary to restraints but are much easier to hande. Testing of the restraint methods with a sheep generay proves that this method works quite efficienty. Testing a horse shoud be done as future work. The computer mode shoud hep to design the restraint system which has to be strong enough to hande horses.

19 . Mechanism of Initiating Motion with ixed Hooves and the Method of Anaysis A standing horse must dispace hooves (or a hoof) and move its egs to initiate horizonta motion. With the hooves fixed, it wi try to pu one eg out of the hoof restraint in order to move it. As sketched in igure.a, when the horse stands normay, the weight (W ) carried by both foreimbs is distributed eveny on the two foreimbs. Weight W wi be in order of,000n (which corresponding to a 00kg mass carried by each of the foreimbs).the ground reaction force (GR) wi be compressive and equa to haf of the weight carried by the front egs. When the horse tries to free the right foreimb, for exampe, the weight wi be switched from the right foreimb to the eft foreimb. If the hoof is unconstrained, the right eg can be raised and moved forward (or backward) and the horse s weight wi be supported by the remaining free egs during this time. If the hoof is constrained then the horse wi use musces to generate tensie forces to pu the eg from the ground. This force, referred to as the breaking force ( B ) is not reated to the horse s weight. The B in the right eg is tensie, whie the eft eg wi carry the compression force being the sum of weight W pus B as shown in igure.b. It is assumed that the eg s skeeton system is sufficienty strong to carry such a compression force without any damage. On the other hand, the tensie force B can reativey easiy either damage the hoof or break the restraint. Therefore, this force wi be the main subject of the anaysis presented. It is demonstrated that the situation at the hindimb is simiar (i.e.: the corresponding B can be determined) to the foreimb. Due to the nature of B, the horse's weight wi not be incuded in the anaysis of a imb fighting mechanism. It shoud be noted that spreading the egs may be an efficient method of constraining the horse. In the position sketched in igure.c, the horse wi not be abe to shift the weight W from the right eg to the eft eg. This is because a centered W supported by the eft eg has to be 3

20 baanced with extra moment, otherwise the anima wi fa. However, there are no sufficienty strong musces to suppy this extra moment (by twisting the upper body, for exampe). This extra moment must come from the ground reaction force supporting the eg. This force wi obviousy disappear at the moment when the horse makes any attempt to raise the eg. Therefore in the spread eg configuration, the anima is not capabe of fighting the restraint as effectivey as in the un-spread configuration. W W W Up Extra moment required W W W + B W : Weight carried by the foreimbs Breaking orce ( B ) (a) (b) (c) igure.: Weight shifting mechanism to free the foreimb To obtain the breaking force, the steps of anaysis approach outined in igure. wi be used. The anaysis resuts wi then be used for a better design of the restraint. The horse is modeed as a inkage system. The initia fu mobiity of such a system is reduced by fixing a four hooves to the ground. With the assumed range of motion at each joint, a possibe eg 4

21 patterns that can be formed within the hoof restraints are identified. When musce forces are appied, the quasi-static breaking force ( B ) generated at the hoof restraint for each pattern is obtained. Then the pattern in which the maximum breaking force can be generated is determined. This pattern is assumed to be the 'best' for the horse in the sense that the horse wi try to use it to free the eg. The breaking force under dynamic jerking is aso obtained and wi be compared with the quasi-static breaking force. Next, more restraints wi be added to competey remove the mobiity of the eg and to prevent forming the patterns that generate arge B at the hoof. inay, the constraint forces wi be minimized by adjusting the restraint anges at each joint. Mode of horse with free mobiity Add initia restraints Skeeta system with initia mobiity Assumed ROM at each joint Add more restraints Pattern Anaysis Appy musce force Quasi-static Puing Dynamic Jerking Remove a mobiity Adjust restraint anges Obtain breaking force ( B ) Optimize constraint force igure.: Scheme of anayzing restraint method 5

22 .3 The Muscuoskeeta System of a Horse Horses move mainy by rotating the imb members around adjacent joints. There are, however, certain imitations paced on the rotation of joints. The shape of the articuar surfaces, tension in extra capsuar igaments, contraction or passive tension in musces and other soft structures around a joint may arrest movement [5]. The imit of rotation is referred as Range of Motion (ROM). The ROM of each joint of the imbs wi be discussed next. When a hoof is constrained to the ground, the degree of freedom of the imb is reduced and the corresponding patterns of the eg motion, which incude ROM of each joint of the eg, can be identified. Musce contraction is the driving force of anima ocomotion. This study assumes the anima can fight against the restraints with its peak isometric musce force. orce generation capacity of major horse musces was reported [6,7]. The peak isometric musce force is defined by M 0 = C PCSA, where C is the maximum isometric stress of the horse skeeta musce taken as 0.3MPa [6] and PCSA is the physioogica cross sectiona area of the musce. The action of a particuar musce force is assumed to be in ine with the musce..4 Mechanics of the Limb Linkage System In this chapter, ony motions of the imb inkage system on the sagitta pane are considered. Motion off this pane is reativey insignificant and contributes very itte to fighting the restraints. The geometric patterns of the imb s motion as we as veocity and acceeration of each part of the inkage system is studied by appying the methods of kinematics. The maximum breaking force is cacuated. It is beieved that the horses may intuitivey find the best geometrica pattern 6

23 to generate such a force. Reationship between the pattern and the breaking force can be predicted either by the kinetics or by the quasi-static anaysis. There wi be no motion in the imb if the musce forces are baanced by the reactions at the restraint or if the ROMs of joints are reached. Then the quasi-static breaking force can be cacuated from equiibrium equations in the form: = 0 and T = 0 (.) The first equation represents equiibrium of forces, where the second represents equiibrium of moments. With some mobiity sti present, the anima may strugge vioenty against the hoof restraint to generate some dynamic jerking force. The dynamic breaking force at hoof can be anayzed with the hep of Newton s aw of motion in transation and rotation for each imb, written symboicay as: = ma and T = Iα (.) where a and α are respectivey the transationa and rotationa acceerations of the members considered. The breaking force can be determined either by soving the static equation (.) or the dynamic equation (.). Simuation software such as ADAMS soves the dynamic probem (.) using the Lagrangian approach which is equivaent to Newton s equation. Detais of the equations of motion in the Lagrange s form can be found in Appendix D..5 Computer Mode of the Horse Dynamic anaysis software can be used to simuate the motion of a horse and its interaction with the restraints. A computer based horse mode was used previousy [4] to study horse free 7

24 ocomotion. This thesis is the first attempt to use a computer anima mode to study the anima s mobiity with initia restraints. Simpe inkage modes and anatomica mode are buit in SoidWorks and its dynamic simuation package COSMOS which soves the dynamics probem using the ADAMS sover. The dynamic anaysis method used is identica to those used in the anaysis of ordinary dynamic mechanica systems. Each part in the anatomica mode is treated as a rigid body and is characterized by its geometric profie, mass, center of gravity and moment of inertia. A system of Lagrangian equations, which is equivaent to (.), is automaticay generated and soved by the computer using a forma description of the constraints, oading forces and initia conditions. The resuts are used in the computer simuation of the motion. More detais about creating the mode can be found in Appendix B and C. 8

25 . ORELIMB RETRAINT METHOD. oreimb Muscuoskeeta Structure and Mobiity A horse foreimb is composed of ong bones suitabe for rotation. Bones of the foreimb incude [5]: Scapua, Humerus, Radius & Una, Metacarpus, Proxima, Midde and Dista phaanges. These bones are inked at shouder, ebow, carpas, fetock, pastern and coffin joints [9] as shown in igure.. The range of motion at each joint is shown in igure. [0,, and ]. In free ocomotion, the foreimb can deveop various configurations that are within these ranges. However, fixing the hooves of the imbs wi significanty reduce the number of possibe configurations and the horse s mobiity. or a inkage system, fixing the dista end of it wi eiminate two degrees of freedom. The horizonta direction freedom of the proxima end of the imb is imited by fixing a the hooves. In addition, the radius and the una are ony aowed to rotate forward from the natura standing position since the extruded oecranon of the humerus imits the ROM of ebow joint. Moreover, the carpa and fetock joints can not extend further. As a resut, the ony mechanism the horse can use to fight the hoof restraint is to fex the ebow. exing the ebow joint is driven by the powerfu biceps which is the most important fexor on a foreimb. Maxima force generation capabiity is estimated to be about,000n. [6] This biceps force can be transmitted to generate a breaking force at the hoof. The forces generated by other musces of the foreimb to fight the hoof restraint 9

26 Scapua Shouder Joint Humerus Ebow Joint Oecranon of Humerus Radius & Una Carpa Joint Metacarpa etock Joint Pastern & Coffin Joint Proxima & midde phaanges Dista phaanx igure.: Skeeton of the horse foreimb 0

27 Natura standing position Extreme rotation imit Shouder Joint A: Ebow A Link Link: Antebrachium 80 Link B 80-5 A. Ebow joint Link ' B. Carpa Joint Link ' : Metacarpus B: Carpa Link ' 70 Link3 ' 30 C 60 Link3 ' D 0 5 Link 3: ' Pastern C: etock C. etock Joint D. Pastern Joint D: Pastern and Coffin igure.: Linkage system of the horse foreimb and the ROM at each joint

28 are significanty smaer. Evauation of these forces in fighting the hoof restraint can be found in Appendix A. The anima can pu the hoof sowy with the biceps force (quasi-static action). The anima can aso pu the hoof by dynamic jerking (i.e. by dynamic action) as observed in the experiment with the restrained sheep. These two ways of generating the B wi be anayzed in the next section.. Mechanica Mode of the Horse oreimb in the Standing Configuration The muscuoskeeta system of the foreimb has been discussed in the previous chapter. In this section, the restrained foreimb of the horse is modeed as a simpified inkage system. Based on anatomic anaysis, it has been assumed that the foreimb mobiity is driven by the biceps musce. The hoof is attached to the ground and the upper body is aowed to move verticay. This mechanica mode shoud be hepfu in answering the foowing questions: What are the possibe eg patterns of initiating the motion and the forces to ift the hoof? What is the best pattern for the horse to deveop the maximum force in fighting the hoof restraint? What are the effects of dynamic jerking in striking against the hoof restraint? How to remove the mobiity of the foreimb in initia restraints by appying more restraints?.. The oreimb Mechanica Mode The foreimb of the horse with hoof restraint can be modeed as a three ink system with a mass at the top as shown in igure.3. The inks were considered undeformabe. In genera, the rues of mechanics (statics and dynamics) of rigid bodies wi be appied. The top mass, estimated at 00kg, is added to represent a portion of the horse s trunk and the upper arm (scapua and humerus) which may be invoved in the foreimb motion. It is assumed

29 that in dynamics, the horse can reocate this mass up or down to maximize the breaking force at the constrained hoof. This mass can aso be ocked at a particuar vertica position by using the upper body musces. In particuar, a quasi-static configuration to produce maximum force wi be deveoped by aowing the top mass to move freey in vertica direction. The motion coud be generated with the force, coming from upper body as shown in igure.3. p Link ( ), ink ' ( ' ) and ink3 ' ( ' 3 ) represent antebrachium, metacarpus and pastern accordingy. The member of ength indicates ink formed when tension on members ' and ' 3 aign them together. Joint A, B, C, D stand for ebow, carpa, fetock and pastern respectivey. Each joint is assumed to be a panar revoute joint. As discussed previousy, it is assumed that ony the biceps wi be used when the horse is attempting to break the hoof s restraint. The action ine of the force is the ine from biceps insertion point (I) on the antebrachium to the origin point E at the shouder joint. 3

30 p E- Shouder joint M Top Mass (M) 00 kg Biceps force: =,000N m A-Ebow joint I-Biceps insertion point Arbitrary Configuration Resting Configuration B-Carpa joint ' ' 3 C etock joint D-Pastern and hoof Joint B igure.3: Mechanica mode of the foreimb 4

31 .. The oreimb Anatomica Computer Mode A computer mode of the mechanica system of the horse foreimb buid up in SoidWorks is shown in igure.4. Motion anaysis is impemented in COSMOS, a software package using the ADAMS sover. E: Shouder Scapuar Brachium A: Ebow Straight : Antibrachium B: Carpa C: etock D: Pastern ' : Metacarpus ' 3 : Pastern Hoof Bent igure.4: Computer mode of the horse foreimb In the computer mode, the top mass in igure.3 is repaced with a join upper arm part, incuding scapuar and brachium, moving in the vertica direction. Hoof is fixed to the ground. Link ( ), ink ' ( ' ) and ink3 ' ( ' 3 ) move as a inkage system forming various patterns as shown in igure.4. More detais on generating the mode can be found in Appendix B. 5

32 ..3 Kinematics of the oreimb Mechanica Mode The mechanica mode shown in igure.3 has three inks with three degree of freedom each (rotation and two components of transation). The inkage is fuy constrained at the dista end and horizontay constrained on the upper end. The inks in between are connected with two revoute joints. Therefore, the mode has 3*3-*--= DO and (in genera) can be controed by two actuation forces. However, when the biceps force is appied on, ' and ' 3 wi be under tension and wi aways aign. Thus there wi be no reative rotation at joint C and the system can be simpified to a sider-crank mechanism with ony one DO. The configuration of such a system depends on ony one DO which can be defined as x (vertica dispacement of joint A), α, or β as denoted in igure.5. Note that now = + and the reationships between α, β and x ' ' 3 can be derived from the foowing two geometric equations: = + H x) ( H )cosα (.) ( x sinα = sin β (.) where H is the distance between A and D in igure.5 when the inkage system is stretched to aign. The ength of ink and ink in the pot are denoted by and. Anges α and β in terms of x is obtained from (.) and (.) as: + ( H x) α = arccos( ) (.3) ( H x) β = arcsin( sinα) (.4) 6

33 E 0 e y ' E A y ' A x E e y 0 e x b m γ I ' E m A γ 0 0 e x b 0 e x b x Puing position α B Resting position H m γ ' I ' A α I e x b cosα β C D a) b) igure.5: Geometric configuration of the foreimb It is assumed that, = 0.496m, = 0.356m, H= + =0.85m. These numerica vaues were obtained from the horse picture used to create the horse mode. See Appendix B for more detais. 7

34 The direction of force m (biceps musce force) is denoted by ange γ. The detai of geometry at the top of the inkage is shown in igure.5b. In particuar, the distance between the ebow joint and the biceps attachment is b = 0.m and distances between the biceps insertion point and the shouder joint at resting position is denoted by 0 e x =0.9m and 0 e y =0.7m verticay and horizontay respectivey. The same distances are denoted as ex and e y in puing position. Then one can obtain ey tan γ = = e x 0 0 ey bsinα e y bsinα = 0 e b + b cosα e b( cosα) x 0 x (.5) 0 e y bsinα Thus, γ = arctan( 0 ) e b( cosα) x (.6) or x in miimeters, the vaues of α, β and γ in degrees are potted in igure.6a,b,c. The vertica dispacement of joint A is zero (x=0) when ink and ink are stretched to aign. Motion at ebow (joint A) on a rea horse is imited by the ROM at the pastern and hoof joint. (Joint D) Therefore, β shoud be smaer than 0 degrees. As a resut, x shoud not be owered more than 0 mm in igure.6b. The corresponding imits imposed on α and γ are 7.5 o and. o respectivey and are marked in igure.6a&c. Since the system has ony one DO, the vaue of ange α (or β) aso defines the compete configuration of the foreimb. rom a the possibe patterns, the pattern to generate maximum breaking force wi be determined in the next section. 8

35 Rotationa imit of α α (degrees) Dispacement imit of Joint A x (mm) a) Angeα versus vertica dispacement of joint A Rotationa imit of β β (degrees) Dispacement imit of Joint A x (mm) b) Ange β versus vertica dispacement of joint A 3.5 o γ (degrees). o Rotationa imit of γ Dispacement imit of Joint A x (mm) c) Angeγ versus vertica dispacement of joint A igure.6: Joint anges versus vertica dispacement of the foreimb 9

36 ..4 The oreimb Quasi-Static Puing If the hoof is fixed then the puing force, referred to as the breaking force ( B ) generated by musces may break the restraint. The abiity to generate this breaking force varies with the configuration of the eg as the motion is initiaized. The reationship between a configuration and the breaking force for the foreimb of the horse is anayzed in this section. irst, the quasi-static case is considered. Quasi-static puing here means that the horse generates a breaking force by constanty puing the eg with the biceps. orces on the inkage system for an arbitrary configuration are shown in igure.7. The bottom member of ength is under tension ony, therefore B = B. Equiibrium equations for the top member of ength can be written as: where M = 0, B sin( α + β ) mb sin( γ + α) 0 (.7) A x = = 0, cos β + cosγ = 0 (.8) B Ax m y = 0, sin γ sin β = 0 (.9) m m is the force generated by biceps attached at I. joint A. orce Ay B Ax, Ay are two components of force at Ax when in compression may reach to the magnitude of about W/ (haf of the weight carried by foreimbs), however, the maximum tensie magnitude of it is generay sma (no major musce pus joint A upward). 0

37 y A Ax Ay a γ Ax A Ay m I α x m b I a = bsin( α + γ ) α B β B β B B β D B D B D igure.7: orce diagram of the foreimb in static puing rom (.7), one has B bsin( γ + α) = B = m (.0) sin( α + ) β Then from (.8) bsin( γ + α) Ax = m (cosγ cos β ) (.) sin( α + β )

38 Since α, β and γ can be expressed in terms of x (by.3-.6), forces B and Ax can be written as functions of x and potted as shown in igure.8 and igure.9. The pots are obtained for m =, 000N. igure.8 indicates that the breaking force at the hoof increases as x decreases or as joint A eevates. However, further anaysis wi show that the increase of B is imited as x becomes ess than about mm and approaches zero. As indicated in igure..9, the vertica force at joint A has to be a puing force required to maintain the equiibrium when x<mm ( Ax <0). This is not reaistic for a horse because there is no major musce on the foreimb to deveop this kind of force as the foreimb has aready been stretched straight. Therefore, for the sake of carity, it is assumed that force Ax can ony be positive (pushing down) in this configuration. The consequence of this is that the maximum B is deveoped when Ax o o = 0, which occurs when x 0 = mm, α 0 =, β 0 = 3, and o γ 0 = 3 as shown in igure..0a, the corresponding diagram of the forces is shown in igure.0b (soid ine). Substituting these vaues in (.0) one obtains Bmax = 0, 60N. The breaking force wi not increase when joint A eevates further up (x<mm). Joint A may move sighty in the horizonta direction as shown in igure..0a (dot ine). B wi stay reativey the same as B Max as expained in igure..0b. If the horse gets tired, the musce force can drop to ' m accompanied by the corresponding reduction of force B. If force Ax is pushing down, which wi happen if 0 β > β, then the diagram of forces is shown in igure.0b3. One can concude that an increase in force B. Ax brings about a decrease in

39 Bmax = 0, 60N B = B (N) or m =, 000N x mm x(mm) igure.8: oreimb hoof s breaking force versus vertica dispacement of joint A or m =, 000 N Ax (N) x mm x (mm) igure.9: Joint reaction force versus vertica dispacement of joint A Ax 3

40 y E x mm A Ay x γ + α γ 0 + α 0 m α B β β 0 D B a) Geometric configuration of the foreimb approaching the top o β 0 = 3, Ax = 0 β < β, 0 0 Ax β β > β, > 0 0 Ax β 0 m β 0 m β 0 B < B max B Max B B Max B Max β ' B ' m α + γ α 0 + γ 0 B Max Ay Ax Ay Ay Ax 0 ) ) 3) b) orce diagram of the foreimb approaching the top igure.0: Anaysis of the foreimb static puing approaching to the top 4

41 inay, based on the anaysis above, it is concuded that the maxima B is generated when x 0 =mm, α 0 =, β 0 = 3, γ 0 = 3 and B max = 0,60N. The corresponding B wi reduce when β is increased or decreased from β 0. Accordingy, force B wi be reduced when joint A is eevated or decined from x 0. igure. is a re-pot of igure.8 showing the decrease of B when x<mm or β < β 0. The anaytica resuts of the reation between the eg pattern and the breaking force generation abiity are aso confirmed by the simuation resuts from the horse mode in COSMOS. B max B = (N) B or m =, 000 N x(mm) igure.: Breaking force in static puing 5

42 ..5 The Breaking orce Due to oreimb Dynamic Jerking In the experiment, the sheep was observed to fight the hoof restraint with dynamic jerking. It is beieved that the horse wi behave simiary. That is, the anima may try to generate the breaking force by the dynamic jerking. The term jerking is used in this thesis to describe the motion of owering and eevating the body quicky (by rotating the eg members) to generate the breaking force dynamicay. The magnitude of the breaking force due to jerking wi be evauated in this section...5. oreimb Jerking by Lowering the Body ( Down Maneuver ) In the sheep experiment, the anima generated jerking by owering the upper body and ebow joint. This motion caused the antebrachium( ), metacarpus and proxima & midde phaanx ( ) to rotate from initia configuration to the fina configuration as shown in igure.. The rotation suddeny stopped when x = 0 mm = 0.0m. As expained in previous section, the fina configuration is defined by the restriction of motion of pastern and hoof joint (joint D). 6

43 m ina configuration p y M x A γ α& & α BInitia configuration β C H D igure.: oreimb in dynamic jerking The dynamic breaking force due to jerking can be determined from an inverse dynamic anaysis if the acceeration and deceeration of the eg during the jerking is assumed. rom a genera sense of motion, one can approximate that the upper eg and body (joint A) and above move down due to gravity at the acceeration rate of a down = g = 9.8m/ s. Based on the motion captured on video during the sheep restraint experiment, the deceeration of the body to stop the eg rotation is estimated to be a stop = 6g = 58.8m/ s. It is assumed that horse wi move at the same acceeration rate. The motion eading to the dynamic jerking can be described with pots in igure.3. igure.3a shows the acceeration and deceeration of the joint A. The change of the acceeration occurs at t = 0.04s to stop the upper arm at x stop = 0. 0m as shown in igure.3c. 7

44 0 Acceeration (meter/s*s) Veocity (meter/s) Time (sec) t g = 9.8m/s a) Acceeration of joint A Time (sec) t b) Veocity of joint A -6g = -58.8m/s X Position (meter) x = 0. 08m x stop = 0. 0m Time (sec) t c) Dispacement of Joint A igure.3: Ebow (joint A) motion in dynamic jerking (down maneuver) 8

45 In the foowing section, the procedure to cacuate the dynamic breaking force due to jerking wi be discussed. The system in igure. satisfies the kinematic equations: x = H cosα + cos ) (.) ( β = sinβ sinα (.3) 0 The anguar veocities of ink and ink can be determined by differentiates of these equations to obtain: x & = sinα & α sinβ & + β (.4) = cosβ & β cosαα & (.5) 0 At t = 0 the veocity x& = v0 = 0 and a down = g = 9.8 m/ s. At t = s, x = m, x & v 0.4m/ s = max =. rom (.) and (.3) att : α 0.8 rad (6.7 o ), β 0.64 rad ( 9.4 o ) = rom (.4), (.5) = α&.93 rad/s, & β 4.rad/ s = = Differentiating both sides of (.4) and (.5) renders: & x = (sinα && α + & α cosα ) + (sinβ && β + & β cos ) (.6) β 0 = (cosβ & β & β sinβ ) (cosαα && & α sin ) (.7) α Substituting.. x = 6g into (.6) and (.7) resuts in the foowing anguar acceerations: & = rad/ s, α& & β =.48 rad/ 690 s One can aso determine the acceeration of centroids of ink and ink from the equations: 9

46 Link: x = c cosα + x = 0.85 [ cos β + ( c )cos ] (.8) c α y = sinα (.9) c c Link: x = H cosβ (.0) c c y = sinβ (.) c c Where c = 0. 5 =0.48 m and c = 0. 5 = 0.78 m are assumed to define the ocation of the centroid of and as shown in igure.4 (Refer to Appendix B to determine the centroid of the foreimb part in the horse mode). By differentiating (.8-.) twice the foowing is obtained: At t, & x C =.55 m/ 46 s & x C =.7 m/ 7 s & y C =.73 m/ 93 s & y C =.74 m/ 94 s The centroid acceeration in x, y direction together with the anguar acceeration are substituted into the dynamic motion equation to cacuate the breaking force due to dynamic jerking. 30

47 m y x γ p M A Ay x Ax M p Ax x α m γ A Ay H α& & α b c B β B By D Bx Bx B By & β c β D B y B x igure.4: oreimb force diagram in dynamic jerking () 3

48 orces appied on the inkage system (igure.4) whie deceerating incude the biceps force ( m ), force on top mass ( ), horizonta force to constrain joint A ( p Ay ) and hoof restraint force ( B ). The motion equations for the top mass, ink and ink are: Top Mass: M& x = (.) A p Ax Link: m & = + (.3) x & c Ax Bx mx m & = + + (.4) y & c Ay my By Link: J && α = c Ax c + By sin α + ( c Ay c ) cosα cosα ( Bx ( m c c b) sin( γ + α) ) sin α (.5) m & = B (.6) x & c x Bx m & = B (.7) y& c By y J c && β = By ( + B y c c ) cosβ cosβ B Bx x c ( sinβ c ) sinβ (.8) where m =, 000N, M =00 kg, m = 6. 7kg, m =. 4kg, = J c 0.37, J c = 0.05, c = 0. 5 = 0.48 m and 0. 5 c = = 0.78 m, o γ =.. By Substituting & x && y, && α, && x &&, & β c, y obtained from the kinematics anaysis the seven c, c c unknown forces in these equations, incuding six reaction forces at each joint and externa force appied verticay on the top mass, can be cacuated. These forces at t are: 3

49 At t = -,589N p = 3,90N = 6,653N B = 6,6N Ax Bx = 3,889N = -903N B =,96N and B = 6,78N Ay By Negative sign of the force means the cacuated force has opposite direction of the x y corresponding force shown in igure.4. igure.5 shows the force diagram pot based on the cacuated resuts. 33

50 At t, orces in Newtons m γ Ax A = 3,90 Ay = 3,889 M p =,589 x α α& & Bx = 6,653 B B By = 903 Bx = 6,653 By = 903 & β β D B y =,96 B =6,78 B x =6,6 igure.5: oreimb force diagram in dynamic jerking () 34

51 m a) Two-ink mode b) Three-ink mode c) Anatomica mode igure.6: oreimb simuation modes The resut obtained from a two inks system descried above agrees we with the COSMOS simuation for the front eg modeed as two inks system as shown in igure.6a. The breaking force obtained from this mode is B = 6, 705 N. The breaking force ( B = 6, 873 N ) obtained using the three ink mode is sighty different as shown in igure.6b. urthermore, the horse foreimb was modeed with an anatomica mode representing the geometry and mass distribution of antebrachium, metacarpus and proxima & midde phaanx ' ' (, ) as cose as possibe. The breaking force obtained from this simuation at t, 3 is B = 5, 6N. One may concude that these three simuation modes have given generay simiar resuts for the breaking force that can be generated by a dynamic jerking. The difference between the forces for the two ink mode and the anatomica mode may be expained as foows: irsty, the joint 35

52 rotation centers in the anatomica mode, which is cacuated automaticay in COSMOS are not exacty aigned with the mass center used in the ink mode. Aso the rotation centers are not in one straight ine with the joints. Secondy, the mass center and the moment of inertia of each part in anatomica mode is automaticay determined in the COSMOS taking into account a specific shape of the part, whie the simpe ink mode assumes mass center in the midde. inay, the DOs of the two inks mode and the anatomica mode are different. Nevertheess the resuts are cose and simuated forces obtained from the anatomica mode wi better approximate the forces generated by a rea horse. This shows the advantage of using a software ike COSMOS for dynamics anaysis with irreguar shaped parts. igure.7: oreimb mode incuding the horse trunk inay, the anatomica mode incuding the trunk as shown in igure.7 is used in simuating the moving down process in dynamic jerking. The interaction between the massive 36

53 trunk and front eg is considered in this mode and biceps musce force is modeed as an actionreaction force between the trunk and the eg. More accurate resut of the breaking force is expected from this mode. Such resuts are shown in igure.8. They indicate that during the motion described in igure.3, the maximum breaking force Bmax 6, 000N is generated, which is about 60% of the force possibe to generate staticay as presented in section..4. These pots indicate that in the down maneuver jerking the force B is not varying much. The maximum vaue of 6,000N is generated at the beginning of the maneuver. As the eg owers down and rotates forward, the breaking force generated on the hoof decreases as the configuration of the eg changes, which agrees we with the breaking force and eg configuration reationship concuded in section..4. In the ast phase with deceeration of -6g, the forces are higher but, due to a favorabe change in the configuration, they are smaer than the B generated at the beginning of the jerking. 37

54 6000 B_ X (newton) Bx (Newton) Time (sec) a) orce B x By (Newton) B_Y (newton) Time (sec) b) orce B y Bmax 6, 000N B (newton) Time (sec) c) The hoof s force B igure.8: The forces due to foreimb dynamic jerking (down maneuver) 38

55 ..5. oreimb Jerking by Eevating the Body (Up Maneuver) It was aso observed that the sheep tried to generate jerking whie rising up the upper body. The upper body motion starts from the owest configuration indicated in igure. as fina configuration and stops at the highest configuration. Since the fina configuration by owering the body now becomes the initia configuration and vise versa, the jerking by eevating the body can be regarded as the maneuver which is inverse to that considerate in the previous section (jerking by owering the body). According to the video, it takes onger time for the sheep to eevate its body than ower it. Simiar situation may appy to the horse as we. Acceerate rate of eevating the body or joint A is assumed to be a up = 0.5g = 4.9 m/ s. When the eg is stretched to the natura standing position, the motion wi be stopped at assumed deceeration rate of 6 g = 58.8 m/ s. igure.9 describes the motion of joint A. The breaking force generated during the potted motion in igure.9 is determined from simuation with the mode shown in igure.7. The resut is potted in igure.0 and it indicates that the maximum breaking force Bmax 7, 00N is generated when the foreimb is stopped at the natura standing position. As can be seen, the maximum B is now 7,00 N, higher than for the jerking down maneuver but sti ony about 70% of the static force generated in puing. The main reason that these dynamic forces are smaer than the static one seems to be restricted character of motion in which the body carries a rather imited amount of kinetic energy. Jerking coud be a habit the animas deveoped naturay when their egs were restrained. However, most probaby the horse wi break free by acting quasi-staticay on foreimbs. 39

56 Acceeration (meter/s*s) g = m / s 6g = 58.8 m/ s Time (sec) a) Acceeration of joint A Veocity (meter/s) Time (sec) b) Veocity of joint A X Position (meter) Time (sec) c) Dispacement of joint A igure.9: Ebow joint (joint A) motion in dynamic jerking (up maneuver) 40

57 Bx (Newton) B_X (newton) Time (sec) a) orce B x By (Newton) B_Y (newton) Time (sec) b) orce B y B (Newton) Bmax 7, 00N Time (sec) c) The hoof s force B igure.0: Breaking force due to foreimb dynamic jerking (up maneuver) 4

58 3. REMOVING THE ORELIMB MOBILITY 3. Effect of Adding Additiona Restraints As mentioned earier, when the hoof is constrained, the foreimb sti has degrees of freedom. The horse can generate about 0,600N of B. In this chapter it wi be shown that this force can be reduced by competey immobiizing the eg in the standing position. Removing a the mobiity of the foreimb can be achieved by adding additiona restraints as indicated in ig.3.. It wi aso eiminate any possibiity to generate the dynamic jerking effects. A A A A m m m m B B B B ϕ C C C C D D D ϕ D d a b c d igure 3.: Additiona restraining of the foreimb's DOs 4

59 In igure 3., the motion of inks can be removed by restraining the motion of joints A, B, and C. A restraint is best appied cose to a joint. Otherwise it wi cause undesired bending of the inks. The restraints appied to carpa and fetock joints ( joint B and C ) are considered. When the carpa joint is fixed as shown in igure 3.b, then none of the inks, can move ', ' 3 under force. If the fetock is fixed as shown in igure 3.c, then inks m ', can sti move. Theoreticay the ebow joint (joint A) coud be fixed in the vertica direction but it woud be difficut in practice. The spreading configuration, in which eg has to support the horse s weight, is shown in igure 3.d. In this configuration it s possibe to immobiize competey the foreimb without additiona restraints because the inks cannot rotate. More detais on this can be found in Chapter orces in the Additiona Restraints Assume that the restraints are in the form of ropes that are attached to the joints under the directions ϕ (at carpa) and ϕ (at fetock) as shown in igure 3.. or the purpose of anaysis, it is assumed that the ropes are tight. Ony the forces due to the action of m (biceps) are considered (some initia tensions in them are negected). The restraint force required at carpa joint can be determined from the static anaysis of ink and of the joint B in the standing U configuration as shown in igure 3.. In this figure, Bx and U By are forces between ink and joint B, joint. L Bx is the force between ink ' and joint B, and is the restraint force at the carpa or ink the equiibrium equations can be written as: U Bx = cos γ (3.) Ay m m + sin γ = (3.) U By U By m a = ( a = b sinγ ) (3.3) 43

60 to obtain: U By mb sin γ = (3.3a) or joint B the equiibrium equations are: = cosϕ + U Bx L Bx, (3.4) U = sinϕ By (3.5) Substituting (3.3a) into (3.5) yieds: mb sin γ = (3.6) sinϕ rom (3.4) one obtains: L b tan γ Bx = m cos γ ( ) (3.7) tan ϕ The above formua indicates that if b tan γ tanϕ then L 0, i.e. ink Bx ' becomes compressed and the restraining force in the carpa joint is capabe of competey immobiizing the eg (no restraint needed at the fetock). or b = 0.m, = m, and the ange of o L attachment γ = 3.5 ( the same numerica vaues as used in section.), force 0 ony if o ϕ 5. That is cabe in igure 3. has to be tightened amost verticay which is somewhat Bx unreaistic. If m =, 000N then under this condition the force in the rope required to satisfy the equiibrium wi be: bsin γ m sinϕ = 0,093N The force in cabe wi decrease to (3.8) sinγ 850 = m b o for ϕ > 5. Link ', however, sinϕ sinϕ L wi be under tension ( = > 0 ) that in turn necessitates the use of the fetock's restraint. Cx Bx or equiibrium of joint C, it is required that 44

61 Joint A m a arm γ b Ay U By Joint B U Bx U By L Bx ϕ (cabe) ' Joint C Cx θ ϕ B (cabe) ' 3 B θ ϕ R Cx Joint D B igure 3.: orce diagram of the foreimb with carpa, fetock and hoof restraints 45

62 Cx B = = sin(80 o ( θ + ϕ )) sinϕ sinθ (3.9) o where θ is the joint ange at fetock as indicated in igure 3.. Here it is assumed thatθ = 5, if horse stands in the resting position. Therefore, sinθ sinθ bsin γ = Cx = m (cosγ ), sin( θ + ϕ ) sin( θ + ϕ ) tanϕ (3.0) sinϕ sinθ bsin γ and B = Cx = m (cosγ ) sin( θ + ϕ ) sin( θ + ϕ ) tanϕ (3.) where Cx is the joint reaction force between joint C and ', is the force in cabe at fetock joint. One can see from (3.6) that is a function of one variabeϕ, whie and B are functions of both ϕ andϕ defined by (3.0) and (3.). The mode in igure 3. was verified by the COSMOS anaysis performed on more detaied modes shown in igure 3.3. The 3-inks mode and the anatomica mode expained earier were used. a) Three ink mode b) Anatomica Mode igure 3.3: Modes of restrained foreimb used in the COSMOS simuations 46

63 orces L Bx,, and B obtained from equations (3.6), (3.0) and (3.) in terms of ϕ and ϕ (for the anaytica mode) are potted in igure 3.4 and compared with the findings from the COSMOS modes. The three inks COSMOS mode resuts indicated by the triange mark agree very we with the anaytica resuts. As mentioned earier, the simuation resuts from the anatomica mode, denoted with circe marks, are sighty different because the properties of each part in the anatomic mode are different than the three inks mode., L Bx (N) L Bx o 5 ϕ (degrees) a) 47

64 o ϕ =30 (N) o ϕ =60 o ϕ =90 ϕ (degrees) B Max = 0, 60N b) B (N) o ϕ =60 o ϕ =90 o ϕ =30 ϕ (degrees) c) igure 3.4: orces on the foreimb versus restraint attachment anges Three inks simuation resut Anatomica mode simuation resut 48

65 These resuts shoud be hepfu in propery choosing the anges of attaching the carpa and fetock ropes. The criterion shoud be to minimize the magnitudes of forces, and B. Aso, one shoud take into account that some siding of the rope is more ikey to happen at the carpa rather than fetock joint. Thus, the vertica component of shoud be minimized as we. The minimum of is atϕ = 90 0, which means that the carpa joint shoud be tightened up horizontay. The foowing resuts were obtained from the COSMOS simuation (anatomica mode) if ϕ is set more reaisticay at 30 o : (Refer to circe mark in igure 3.4) = 99 N (horizonta) = 6,884 N B = 4,768N Note that force B is ony about 40% of Bmax obtained in section for the case of quasistatic puing without additiona restraints. This significanty reduces the risk of breaking the hoof restraint. If the ropes deformation is sufficienty sma (or the ropes are sufficienty strong) then the mobiity of the eg is totay removed. That is, propery designed restraining ropes and the hoof restraint shoud be capabe of neutraizing and controing any effort of the biceps to free the foreimb. 49

66 4. HINDLIMB RESTRAINT METHOD 4. Hindimb Muscuoskeeta Structure and Mobiity The hindimb provides most of the propusion for the horse to move forwards. The propusion is deveoped by a powerfu backward swing of the imb with the hoof contacting the ground. This mechanism uses strong musce, such as biceps femoris, to deveop the forces that can ift the hind hoof. It becomes the most prominent fighting pattern used by the horse in free itsef from the hoof restraint. The hindimb of a horse is composed with Hip bone, emur, ibua and Tibia, Metatarsa, Proxima, Midde, and Dista Phaanges (hoof). These bones are connected at hip joint, stife joint, hock joint, tarsa joint, pastern and coffin joint as shown in igure 4.. [9] The methodoogy to anayze mechanics of hindimb is simiar to that used in Chapter to examine the foreimbs. The range of motion at each joint of the hindimb is potted in igure 4.. When the hind hoof is fixed, extension at stife joint and hock joint is restricted by the extruded cacaneus. Overextension at pastern and coffin joint is aso imited. As a consequence, straightening the eg is not permitted. The ony way to fight the hoof restraint is to fex the stife and hock joint with the biceps femoris musce as shown in igure Mechanica Mode of the Hindimb in the Standing Configuration It is obvious that the standing configuration of the hindimb is very simiar to a mirror image of the foreimb in a bent position. When the hoof is fixed, the puing 50

67 Hip Joint emur Stife Joint ibuar &Tibia Cacaneus Hock Joint Metatarsa Proxima, Midde & Dista Phaanges Metatartus Joint Pastern and hoof Joint igure 4.: Hindimb skeeta structure 5

68 : Sacroiiac Joint Natura standing position Extreme rotation imit E: Hip Joint A: Stife Joint A Link 5 40 B Link Link 70 5 Cacaneus Link ' B: Hock joint A. Stife joint B. Hock joint Link ' C: Metatartus Link3 ' D: Pastern & Coffin Link ' C 80 Link3 ' C. Metatartus joint Link3 ' 0 D 30 D. Pastern and coffin joint igure 4.: Linkage system of hindimb and the ROM at each joint emur 5

69 force generated by biceps femoris and transmitted to the hoof wi generate the breaking force on the hoof. Athough the biceps femoris ooks stronger than the biceps musce in the foreimb anaysis, their measured PCSA is amost the same [6,7]. orce generation capacity of the musce is aso estimated at,000n from the musce force and PCSA reationship function (see Section.3). If the hoof of the hindimb is constrained, the forces of other musces add very itte in heping to ift the hoof. More expanation on roe of various musces on the hoof restraint can be found in the Appendix A. Again, the breaking force generated in the quasi-static action and dynamic jerking wi be anayzed. Immobiizing the hindimb in a particuary position wi be discussed in detai. 4.. The Hindimb Mechanica Mode The hindimb of the horse is modeed as a three ink system with a mass on top as shown in igure 4.3. The mobiity of the imb with the hoof restraint is driven by the force generated by the biceps femoris ( ). The hoof is fixed to the ground and the hip of the horse is aowed to move verticay. m The top mass, estimated at 00kg, is added to represent a proportion of the horse s trunk and hip weight which may be invoved in the hindimb motion. Link, ' and ' 3 represent, fibua & tibia, metatarsa, and proxima & midde phaanges accordingy. Joint A, B, C, D stand for stife joint, hock joint, tarsa joint, pastern & coffin joints respectivey. Each joint is assumed to be a panar revoute joint. The action ine of the biceps femoris is the ine from the musce s insertion point (I) on the tibia to the origin point at the hip joint (E). 53

70 M: Top mass 00kg E: Hip Joint A: Stife Joint m =, 000N Link I B: Hock joint Link ' C: Tarsa Link3 ' D: Pastern coffin joint B igure 4.3: Mechanica mode of the horse hindimb 54

71 4.. The Hindimb Anatomic Computer Mode A computer mode of the mechanica system of a horse hindimb buid up in SoidWorks is shown in igure 4.4. This mode aso consists of essentiay three inks, but the inks have more anatomicay correct shapes. In the computer mode, the top mass in igure 4.3 is repaced with the hip of the horse, free to move in the vertica direction. Hoof is fixed to the ground., ' and ' 3 move as a inkage system. Geometry profie and physics properties of each part of the imb are defined in SoidWorks. Joint ocations are defined based on the anatomy of average horse. E: Hip Joint A: Stife Joint : ibuar & Tibia B: Hock Joint ' : Metatarsa ' 3 : Proxima & Midde Phaanges Hoof C: Metatartus D: Pastern Coffin Joint igure 4.4: Overview structure of the hindimb 55

72 4..3 The Hindimb Quasi-Static Puing As mentioned earier, the diagram of the hindimb mode shows simiarity with a mirror image of a foreimb mode. The biceps femoris force m pus ink (ibuar & Tibias) and generates the breaking force that may break the hoof restraint. igure 4.3 shows the hindimb standing configuration. In chapter it was concuded that the horse generates the maximum B if it pus the eg straight up from the standing configuration. or the hindimb, straightening the eg is restricted by the ROM at joint D and joint B. (refer to igure 4.) The force B under the restriction wi be determined from static anaysis on the hindimb. igure 4.5 shows the force diagram on the hindimb. As the biceps femoris pus ink, there wi be tension in ink ' and ink3 ' that stretch them forming a ine, or ink as shown in the pot. Note that and denote the ength of ink and ink. H and L are vertica and horizonta distances between joint A and joint D. In particuar, the distance between the hip joint and the biceps femoris attachment point (I) is b and distance between the stife joint (Joint A) and the hip joint is denoted by 0 e x and e 0 y, verticay and horizontay respectivey. These numerica vaues are obtained from the measurement with the horse mode buid up in SoidWorks and are taken as: H = 0.783m, L = 0.053m, = 0.397m, 0 e x = 0.305m, e 0 y = 0. 39m = 0. 45m, b = 0.m, 56

73 57 igure 4.5: orce diagram of hindimb quasi-static puing H A B D D I D I B β φ β γ L α A B α φ β φ γ a B b sin( γ ) φ α + + = b a 0 y e 0 x e m m B B B B Ax Ay E φ

74 Then anges α, β, γ, φ in the configuration pot in igure 4.5 are cacuated based on the geometric reations of each member. The anges are shown as: o o α = 5, β = 4, o γ = 8, o φ = 3.8 The ower member of ink is under tension ony, therefore B = B. Equiibrium equations for the top member of ength are written as: M A = 0, B sin( α + β ) mb sin( γ + α + φ) = 0 (4.) where, m =, 000N.Thus, B is obtained as B bsin( γ + α + φ) = B = m 7, 50N sin( α + β ) (4.) It shoud be noted that breaking force that can be generated at the hindimb is about 70% of the maximum breaking force that can be generated on the foreimb The Breaking orce Due to Hindimb Dynamic Jerking The sheep in the experiment was observed to move its hip up and down dynamicay whie trying to free itsef. It is beieved that it was done to generate dynamic breaking forces. The magnitudes of the dynamic breaking force are to be determined in this section Hindimb Jerking By Lowering the Hip (Down Maneuver) The anima can quicky ower hip and the stife joint (Joint A) so that the fibuar & tibia (ink), metatarsa and proxima phaanx (ink) can rotate from the initia configuration to the squat configuration as shown in igure 4.6. The rotation wi stop at the squat configuration due to ROM at pastern and coffin joint generating impact forces. 58

75 p M A m Link M A B m Initia Configuration Link ' Link B Squat Configuration Link3 ' D Link igure 4.6: Hindimb in dynamic jerking Simiar to the motion of the front eg, it is assumed that motion of owering the hindimb is initiaized with the gravity force of the body at the acceeration rate of a down = = g 9.8m/ s. The vertica motion is assumed to stop when joint A is owered at x stop 0.4m with the deceeration of astop = 6g. igure 4.7 describes the motion of owering the hip in the jerking. 59

76 Acceeration (meter/s*s) a down = g = 9.8 m / s a stop = 6g = 58.8 m/ s a) Acceeration of joint A Veocity (meter/s) b) Veocity of joint A c) Dispacement of joint A igure 4.7: Stife joint (joint A) motion in dynamic jerking (down maneuver) 60

77 Bx (Newton) B_ X (newton) Time (sec) a) orce B x 5000 By (Newton) B_Y (newton) Time (sec) b) orce B y B (Newton) Bmax 8, 500N Time(sec) c) The hoof s force B igure 4.8: orces due to hindimb dynamic jerking (down maneuver) 6

78 The anaysis method used to determine the dynamic breaking force on the hindimb due to jerking is identica to the one used when anayzing the foreimb in Chapter. In this chapter, the jerking effects in hindimb are simuated with a mode shown in igure 4.4. igure 4.8 pots the breaking force due to the jerking as the hip and stife joints move down. The simuation resut indicates that maximum breaking force of Bmax 8, 000N is generated as the hindimb initiates jerking at the natura standing position Hindimb Jerking by Eevating the Hip (Up Maneuver) After the eg is forced to stop at the squat configuration as shown in igure 4.6, the horse might eevate the hip up to return to the initia standing position. or the sheep, it was observed that it takes onger to ift the hip in the jerking than owering it down. Assuming that the horse wi behave simiary, the acceeration to ift the hip is then approximated to be aup = - 0.5g. As the eg returns back to the initia standing position, a deceeration is assumed at a stop = 6g to stop the motion. This is described in igure 4.9 and the maximum breaking force generated in this period is at Bmax = 7, 00N when the rotation is stopped cose to the natura standing position as shown in igure

79 Acceeration (meter/s*s) a up = 0.5g = 4.9m/ s Time (sec) a) Acceeration of joint A a stop = 6g = 58.8m / s Veocity (meter/s) Time (sec) b) Veocity of joint A X Position (meter) Time (sec) c) Dispacement of joint A igure 4.9: Stife joint (joint A) motion in dynamic jerking (up maneuver) 63

80 Bx (Newton) B_X (newton) Time (sec) a) orce B x 4000 By (Newton) B_Y (newton) Time (sec) b) orce B y 8000 B 7, max 00N 7000 B (Newton) Time(sec) c) The hoof s force B igure 4.0: orces due to hindimb dynamic jerking (up maneuver) 64

81 In summary, maximum breaking force generated during the jerking can reach to about 8,500 N which is about,300 N higher than the breaking force generated by static puing. Thus, the jerking mechanism deveoped intuitivey by the anima is proven to be usefu in fighting the hindimb s restraints. To prevent the anima from generating high breaking force, more restraints shoud be added on the imb to immobiize it. Detais of removing the tota mobiity on the hindimb wi be discussed in the next chapter. 65

82 5. REMOVING THE HINDLIMB MOBILITY In this chapter, compete removing of the hindimb mobiity is considered. It has been found in the sheep restraint experiment that the hock joint restraint can immobiize the joint when adding the restraint propery. The required constraint forces in the eg spreading configuration wi be investigated. y x Ax A A Ax m ϕ ' B Moving down C ' ' C 3 3 D d D a) Natura standing position b) Stretched to aign position ϕ B ' igure 5.: Adding hock restraint on the hind imb in two configurations 66

83 5. Effect of Adding Hock Joint Restraint in Natura Standing and Stretching Configurations In the sheep restraint experiment, the hock restraint cannot competey immobiize the joint when sheep stands naturay in the configuration shown in igure 5.a because of possibiity of sideways motion. However, by spreading the sheep s egs (as the configuration in igure 5.b) the sideway mobiity of the eg seemed to have been removed and the hock restraint successfuy immobiized the joint and the whoe hind imb. In order to expain the above phenomena the potentia motion of the imb in these two configurations is anayzed. In igure 5.a, hock joint (joint B) tends to move down by the gravity force Ax. The hock restraint force under the direction of ϕ does not act contrariy to this motion. In addition, it is hard to restrain joint B as joint C can fex. exion of joint C can be imited when the hoof (D) is fixed at the distance d from the natura position. Aso, the visua inspection of the sheep indicated that the rope at B forced ink, ink and ink3 amost to aigned as shown in igure 5.b. Therefore, in the anaytica mode these inks are configured in a straight ine. Detais to determine the required restraint forces in the rope attached at B and the breaking force at D wi be discussed in the foowing section. 5. Required Restraint orce at Hock Joint orces exerted on the hindimb's inks in the aigned configuration are shown in igure 5.. The equiibrium equations for ink can be written as: U = 0 (5.) Ax + Bx mx U = 0 (5.) Ay + By my U U Bx sinα + By cosα mb sin( α + γ ) = 0 (5.3) 67

84 68 igure 5.: orce diagram with hock restraint A Ax A B Joint B B B D U Bx U B L B D L B B B D α Ay Ay Ax U By γ γ m m U Bx U By α α L B α ϕ x y d

85 where U Bx and U By are joint reaction force between ink and joint B. The foowing numerica vaues obtained from standing horse image that was used to buit the mode are used for the hindimb mode: b=0.m, =,000N, = 980 N, = m, o =0.45 m, α = 9, m Ax o γ = 8.6. The three unknowns obtained from (5.-5.3) are: U = 9,444 N, = 53 N, = 4, 04 N U Bx Substitute L B U Bx and By Ay U By into equiibrium equation for joint B: U cosα + cosϕ = 0 (5.4) Bx U L sinϕ By sinα = 0 (5.5) where is the constraint force at hock joint, B ink ' and joint B and is equa to the breaking force B. Both and L B can be expressed in term of variabe ϕ as: L B is the joint reaction force between U U By + Bx tanα = and (5.6) sinϕ + cosϕ tanα U U Bx tanϕ L By B = B = (5.7) sinα + cosα tanϕ Simiary as for the foreimb the COSMOS three inks mode and the anatomica mode of the hindimb shown in igure 5.3 were used to vaidate the above formuas. orces and B as functions of ϕ according to (5.6) and (5.7) are potted in igure 5.4 and 5.5 with soid ines. The COSMOS simuation resuts obtained from three inks mode and the anatomica mode are marked with triange and circe marks respectivey as we. 69

86 a) Three inks mode b) Anatomica mode igure 5.3: The COSMOS modes of hindimb with hock and hoof restraints Three inks simuation mode resut Anatomica simuation mode resut (N) Cacuated resut ϕ (Degrees) igure 5.4: Required hock reaction forces versus the restraint attachment ange 70

87 B (N) Three ink mode simuation resut Anatomica mode simuation resut Cacuated resut ϕ (Degrees) igure 5.5: Required breaking force versus restraint attachment ange In genera, both simuation resuts agree we with the anaytica resut. These resuts indicate that increasing ϕ causes the hock's restraining force to decrease and the breaking force to o o increase. A good compromise seems to be the range at ϕ = with both the hock and o hoof restraint forces are simiar and equa to about 5,000N. If ϕ increases to 45, then drops to 3,950N, but B increases to 7,00N. 7

88 6. THE SHEEP RESTRAINING EXPERIMENT Because of the cost and safety invoved, the anima mobiity experiment is preformed with a sheep. Sheep have simiar skeeta muscuar system as horses, and use simiar strategies to initiate motion. Aso, it is beieved that sheep wi react somewhat simiary to restraints as horses. The test of restraining a sheep was conducted at the Western Coege of Veterinary Medicine at the University of Saskatchewan on a heathy adut sheep without using any drug. The whoe experiment was recorded on video for the use of further anayses. Equipments used in the test incude one genera cinica purpose sheep restraint cart, a hater for constrain the sheep s head, four ceats instaed on the bottom pate of the cart to fix the hooves and two ropes to restrain the sheep s hock joints. 6. Appying Initia Restraints 6.. Sheep Cart The sheep was first ead into a restraint cart as shown in igure 6.. Essentiay, the sheep was restrained against sideways motion by the neck ony. Standing in the cart, the sheep was sti free to move in the space between the side was. 7

89 igure 6.: Sheep cart 6.. Hoof Restraint The hoof restraints were critica for controing the sheep's behavior in the experiment. It was observed that without the hoof restraint, the sheep kicked the hindimb vioenty when an operator tried to ift its right hindimb as shown in igure 6.. igure 6.: Sheep fighting without hoof restraints A customized design of the hoof restrain with ropes and ceats was deveoped. In order to fasten the restraint rope quicky and tighty, ceat was used in a way as shown in igure 6.3a. 73

90 Each rope was attached at the coffin joint with a bowine knot as shown in the pot. The rope went underneath the pate of the cart through a nut preventing rough contact between the rope and the edge of the bottom pate. The rope pued the foot down and pressed it against the foor when it was tightened up with the ceat. Ceat coud ock the rope with the teeth on the surface of roers. To immobiize the hoof the rope shoud be positioned precisey in mid cauda pane of the foot. Otherwise the hoof was not eveny pressed against the foor, which made the anima uncomfortabe. Attention shoud be paid to avoid pacing the rope in the interdigita space of the hoof as shown in igure 6.3b. Bowine knot a) Recommended hoof restraint Ceat b) Hoof restraint to be avoided igure 6.3: Hoof restraints 74

91 6..3 Head Restraint With fixed hooves but no head restraint, the sheep coud generate significant back and forth body motion. Such motion was depicted in igure 6.4. This was reduced when the head was restrained with a hater as shown in igure 6.5. To eiminate the side movement, the ropes extended from both sides of the hater were tightened to the cart. Aso it prevented the sheep from raising its head up and down. The sheep seemed to be quite comfortabe with this constraint in pace and tight. igure 6.4: Sheep body movement without the head restraint igure 6.5: Head restraint 75

92 6. Mobiity of the Initiay Restrained Sheep ocus of this phase of experiment was to observe the anima s behavior with the head and hooves immobiized. The overview of the initia restraints is shown in igure 6.6. The mobiity of the foreimbs and the hindimbs, and how the sheep woud use these body parts to fight the restraints were of particuar interest. igure 6.6: Overview of the sheep initia restraints 6.. oreimb Mobiity Quasi-Static Puing In Chapter, it was concuded that the best way for the anima to generate the maximum breaking force on the fore hoof woud be to use the biceps to staticay rise up and bend the foreimb. Aso, it was concuded that the anima woud intuitivey find the best pattern to deveop this force. The behavior of the sheep in the experiment confirmed the above concusions. The sheep shown in igure 6.7a was standing naturay under the initia restraint. In igure 6.7b, the anima shifted a the weight on other three egs, and then raised the shouder of the eft foreimb. The quasi-static puing pattern seen in this figure is amost identica to the 'best' puing pattern obtained in Chapter in which the maximum breaking force was generated. 76

93 a) Norma standing b) Sight raise and bending igure 6.7: Quasi-static puing on the sheep foreimb 6.. oreimb Mobiity Dynamic Jerking oreimb dynamic jerking as discussed in Chapter was aso observed in the experiment. The imb jerked very quicky backward and forward severa times in an attempt to break the hoof restraint. These movements are captured in igure 6.8. Then the sheep returned to the static puing. This may be considered as evidence that the atter is a better strategy to use to free itsef from the restraint. 77

94 a) oreimb jerking backward b) oreimb jerking forward igure 6.8: Dynamic jerking on the sheep foreimb 6..3 Hindimb Mobiity Quasi - Static Puing According to the hindimb functiona anaysis, the anima shoud try to use the biceps femoris to ift the hindhoof. However, this was not obvious on the hindimb as seen on the foreimb. In the hindimb, the anima woud rather stay in the natura position and generate the static breaking force from this position due to the difficuties of raising the hind imb and stretching it as discussed in Chapter 4. It shoud be noted that no significant change of the eg pattern is needed 78

95 to do so. Therefore, it is more difficut to observe whether or not such a force is actuay there and for how ong Hindimb Mobiity Dynamic Jerking In the experiment, the sheep was seen to move its hip up and down to create dynamic jerking effect as shown in igure 6.9. This jerking is driven by the weight on top of the imb and the puing of the biceps femoris. Aso, when the sheep jerked, the sheep cart was shaking sighty accompanied by the noise of ratting parts (the noise can be heard in the video). It indicates that greater forces were created at the bottom pate of the cart when the hindimb was jerked than the foreimb. igure 6.9: Dynamic jerking on sheep hindimb 6.3 Adding the Hock Restraint to Immobiize the Hindimb To reduce the dynamic jerking, hock joint restraints were added as shown in igure 6.0. One end of the rope was tightened around the hock joint whie the other end was dragged through the bottom pate of the cart by operators and tightened up. 79

96 igure 6.0: Sheep restrained with hock restraints and hoof restraints When the hindimb stood in the natura standing position, the rope was amost horizonta, which makes the hock restraint not competey preventing side motions. Consequenty, the sheep managed to sit down as shown in igure 6.. Aso, according to the anaysis in Chapter 5, the joint rotation can be ocked ony when the hindimb is stretched in the aigning configuration. This wi be discussed in more detais in the next section. igure 6.: Sheep free itsef from improper hock restraint 80

97 6.4 Restraining the Sheep in the Legs Spread Position As discussed in Chapter, restraining the anima in the egs spread position shoud be a more efficient method to immobiize the anima. When the egs are spread, it is difficut for the anima to switch the weight support from four to three egs. With a four egs sti supporting the body weight, it is hard for the sheep to fight the restraint. In the experiment, first the fore hooves were fixed to the corner of the cart to spread foreimbs apart and were moved sighty forward. As a resut, extra mobiity of the foreimb, essentiay the bending at the carpa joint predicted in Chapter 3 was eiminated in the egs spread position. Therefore additiona restraint on the fore imb was not needed. Next, the rear hooves were spread apart and fixed to the bottom as shown in igure 6.. In this configuration, hindimb was stretched to aign at the hock joints as shown in igure 6.3. Joints motion was ocked in this configuration. The hock restraint was tightened up with a reativey sma effort of the operators. It was sufficient to immobiize the hock joint as we as the whoe hindimb. Summarizing the experiment, the sheep seemed to be competey immobiized in the position shown in igure 6.. It was possibe to move and turn the cart without any observabe motion of the anima s body or egs (with the exception of that caused by breathing). Aso there was no reaction to touching or even sighty pushing the body. 8

98 Hock Restraint igure 6.: Sheep restrained in egs spread position Hock Restraint igure 6.3: Sheep hindimb stretched to aign The anima seemed to be comfortabe with the position for about 5 minutes before it started moving and kicking again after the restraints were reeased. The ropes can be retightened quicky (and the hooves ocation can be modified) if the ceats are propery positioned. 8

99 7. CONCLUSION AND UTURE WORK Methods of removing the horse's mobiity in its natura standing position are studied in this thesis. Various methods of restraining the horse are evauated anayticay and by computer simuation. The findings have been tested experimentay on a sheep. The ROMs at the joints of the horse egs imit the patterns of initiating the motion especiay when the hoof of each eg is fixed to the ground. A simpe inkage structure is used to simuate such a motion. orces generated by the horse and forces transmitted to the hooves (referred to as the breaking forces) at quasi-static and dynamic (dynamic jerking) attempts to initiate the motion from the natura standing position are determined. The anaysis assumes that the egs' configurations can change within the imits imposed by ROMs. The resuts indicate that for the foreimb the static force puing the hoof may be greater than the force generated by dynamic jerking. On the other side, the hindimbs are capabe of generating more breaking force dynamicay than staticay. The horse's egs can be competey immobiized in the standing configuration by adding more restraints to particuar joints (in addition to the hoof restraints). It eiminates the dynamic jerking and aso reduces the static forces that the horse can generate. The anaysis, the computer simuation and the experimenta observations a indicate that such a method of the anima's restraining shoud be very effective. The forces required to restrain each joint that are significant to the horse's mobiity are evauated. urthermore, these forces can be reduced by optimizing the anges of 83

100 attachment of the restraining ropes to the joints. In addition, spreading the egs makes much harder for the anima to fight with the restraints. This is because it substantiay imits the anima's abiity to switch weight from one eg to another when preparing to initiate the motion. A the above concusions were confirmed by the experiment conducted on a sheep. The anima restrained by ropes that fastened a the hoofs and significant joints was standing sti without any apparent discomfort for a time that seemed to be sufficienty ong for the imaging appication, proposed by the Biomedica Imaging and Therapy Beamine at the Canadian Light Source. This essentiay proves the feasibiity of the approach anayzed theoreticay in this thesis. uture pans shoud incude testing a horse. In particuar, one shoud examine how suitabe are the ropes and ceats to immobiize the anima that is much bigger than a sheep. A sketch of a possibe horse restraint patform is presented in igure 7.. A fat bed is needed to fix the hooves. A the ropes restraining the joints can aso be attached to the bed. However, an additiona structura member attached to the bed is required to immobiize the head (otherwise the horse wi use it to generate some dynamic forces when trying to free itsef), which can be in the form of a simpe frame shown on the sketch. The horse s head and neck wi be restrained with the hep of a head hater attached to the frame. Detais of the horse hoof restrains design wi have to be worked out. Hoof pads that can side on the patform may be added to assist spreading the horse s egs apart. Aso, methods of quicky attaching and detaching the ropes to the horse's joints without harming the anima shoud be investigated, most probaby by experimentations. 84

101 igure 7.: Horse restraint patform The breaking forces to be generated by the horse during possibe strugging actions were obtained 'theoreticay' in the thesis. These forces coud be verified experimentay by appying the strain gages or other types of force measurement devices. If the experimenta tests confirm that the horse's restrain in the natura standing configuration is satisfactory, then one may think about designing a system to restrain the horse with one ifted eg, for exampe. Such a position may be required for some imaging procedures. rom the computer simuation viewpoint a mode that can recreate a 3D motion of the whoe horse might be worth to deveop. Athough the horse's mobiity seems to be essentiay confined to the sagitta pane, a better understanding of possibe sideway movements shoud be hepfu in refining the restraint system. 85

102 inay, the anaysis and computer simuation methods proposed in this thesis coud be extended to study the restraint methods for other animas, which can be done by simpy modifying the anatomica structure and function used in the mode. 86

103 LIST O REERENCES [] Hodson E., Cayton H.M., Lanovaz J.L., The foreimb in waking horses:. Kinematics and ground reaction forces, Equine Veterinary Journa, 000, v 3, pp87-94 [] Hodson E., Cayton H.M., Lanovaz J.L., The hindimb in waking horses:. Kinematics and ground reaction forces, Equine Veterinary Journa, 00, v 33, pp38-43 [3] Cayton H.M., Advances in motion anaysis, Veterinary Cinics of North America: equine practice, 99, v 7, pp [4] van den Bogert, A.J. Computer Simuation of Locomotion in the Horse PhD Thesis, 989 [5] Dyce K.M., Sack W.O., Wensing C.J.G., Textbook of Veterinary Anatomy, nd ed. WB Saunders, 996 [6] Payne R.C., Veenman P., Wison A.M., The roe of the extrinsic thoracic imb musces in equine ocomotion, Journa of Anatomy, 005, v 06, pp93-04 [7] Payne, R.C., Hutchinson,J.R., Robiiard, J.J., Smith, N.C., Wison, A.M. unctiona speciaisation of pevic imb anatomy in horses, Journa of Anatomy, 005, v 06, pp [8] Wison A.M., McGuigan M.P., SUA, van den Bogert A.J. Horse damp the spring in their step, Nature, 00, v 44, pp [9] Cayton H.M., ood, P.., Coor Atas of Large Anima Appied Anatomy, Mosby-Wofe,

104 [0] Ramón, T., Prades, M., Armengou, L., Lanovaz, J.L., Muineau, D.R. and Cayton, H.M., Effects of athetic taping of the fetock on dista imb mechanics, Equine Veterinary Journa, 004, v 36, pp [] Cayton, H.M., Sha, D.H. and Muineaux, D.R., Three dimensiona kinematics of the equine carpus at trotting horses, Equine Veterinary Journa, 004, v 36, pp [] Cayton, H.M., Singeton, W.H., Lanovaz, J.L. and Prades, M., Sagitta pane kinematics and kinetics of the pastern joint during the stance phase of the trot, Veterinary Comparative Orthopedics and Traumatoogy, 00, v 5, pp5-7 [3] Rooney, J.R., The Mechanics of the Horse, R. E. Krieger Pub. Co., 98 [4] Hedge, J., Wagoner, D., Horse Conformation, Structure, Soundness, and Performance, The Lyons Press, 999 [5] Piiner, S. Emhurst, S., Davies, Z. The Horse in Motion, Backwe Pubishing, 00 [6] Buchner, H.H.., Saveberg, H.H.C.M., Schamhardtt, H.C., Barneved, A., Inertia Properties of Dutch Warmbood Horses, Journa of Biomechanics, 997, v 30, pp [7] [8] Marion, J., Cassica Dynamics of Partices and Systems, nd Edition, Academic Press, 970 [9] Haug, E. J. Computer Aided Kinematics and Dynamics of Mechanica Systems, Ayn and Bacon,

105 APPENDIX A. EVALUATION O LIMB MUSCLE ORCES IN IGHTING THE RESTRAINTS It is assumed in the thesis that biceps and biceps femoris pay the most important roe in generating the force to free the horse eg from the restraints. orces generated by other major musces on the imbs are not incuded in the mode since their contribution in fighting the restraints are very itte when compared with the biceps and biceps femoris musces. A brief justification of the above assumptions is presented in this appendix. A. oreimb Musces Besides biceps, major musces in the foreimb incude Brachiocephaicus (BO), Serratus Ventrais Cervicis (SVC), Serratus Ventrais Thoracis (SVT), Latissimus Dorsi (LD), Triceps (T) on the upper arm, Extensors group (E), and exors group () on the ower imb. [5], [4],[5] The upper arm musces are used to protract or retract upper arm as shown in igure A.. [3]. However, ranges of protraction and retraction are not enough to stretch the eg members in tension, thus has no effect on puing of the hoof restraints. Lower imb extensors such as Common Digita Extensor (CDE) (igure A.a) may generate force to ift the hoof. But these musces are not strong compare with the biceps and this force is ignored in the mode (maximum force generation capabiity for CDE is about,000n [6]). The fexors group (igure A.b) has severa stronger musces such as deep digita fexor (DD) and superficia digita fexor (SD). When the hoof is fixed to the ground, forces puing the eg wi ony push the hoof to the ground. 89

106 BO SVC+SVT T LD Protraction Retraction a. Musces for upper arm protraction b. Musces for upper arm retraction igure A.: Upper foreimb musce forces in foreimb CDE DD+SD a. Extensor b. exors igure A.: Lower foreimb musce forces 90

107 A. Hindimb Musces Simiar situation appies to the hindimb as we. or a musce forces incuded in igure A.3 ( Gutaeus Mediais = GM, Quadriceps emoris = Q, Semitendinosus = ST, Gastronemius = GN) [5],[4],[5] Their infuence to the hoof is restricted by the rotation imit at hock joint. Just ike foreimb, the force from ower extensor musces shown in igure A.4a (Latera Digita Extensor = LDE) is ignored in the mode [7]. The stronger digita fexor in igure A.4b (DD, SD) wi ony ed the hoof to push the ground when the hoof is fixed to the ground. Gutaeus Mediais Semitendinosus Quadriceps emoris Gastrocnemius a. Hip and Stife joint musces b. Hock Joint Extensor igure A.3: Upper hindimb musce forces 9

108 LDE DD+SD a. Digita Extensor b. Digita exor igure A.4: Lower hindimb musce forces 9

109 APPENDIX B. GENERATING THE HORSE MODEL IN SOLIDWORKS A 3D mode of a horse is buit up based on the twenty-six segment horse mode given in igure B. [6]. This is a mode of a Dutch Warm Bood horse been introduced as an average horse mode used in previous horse ocomotion studies. igure B.: Twenty-six segment mode of a Dutch Warm Bood horse B. Defining the Geometric Shape of the Horse In order to create a horse computer mode that is simiar to the horse shown in igure B., A picture of a rea Dutch Warm Bood [7] horse is used as a background image in each segment s part fie. In each part fie, mode shoud be scaed to read 56cm for the horse trunk as given in Butcher s note (Tabe ). This procedure unifies the scae in each part fie. 93

110 Tabe : Horse Body Segment Properties (Mass, density, reference ine, reference ength) The 3D segment is created from the cross-sectiona area profies as shown in igure B.a. These profies (ovas) are potted according to the width of each segment in various height eves in the sagitta pane. Then commend oft is used to connect each cross-sectiona profies with smooth curves to create a 3D object as shown in the figure. The ength of each segment is the distance between two joints of corresponding eg member in the background image. The entire horse is buit in an assembe fie gathering a segments of twenty-six part fies. a) b) igure B.: Creating 3D horse mode 94

111 B. Physica Properties of Body Segment Density of each part provided in Tabe is used in the computer mode. Soidworks can then cacuate the mass of the segment from the product of the voume and the density of it. When the cacuated mass in the computer mode has significant difference with the mass isted in Tabe, the short axis of the ova shape profie wi be adjusted ti the mass in the mode agrees with the mass isted in Tabe. Centroid of each segment is determined automaticay in Soidworks. Centroid position of some segments wi be used in the simuation program to determine the dynamic reaction force. 95

112 APPENDIX C. MOTION SIMULATION CosmosMotion, the dynamic motion simuation software can incorporate with mode created in SoidWorks to simuate motion of the inkage system, representing the horse s skeeta structure. Constraints, musce forces and some initia movement conditions and body resistance to the motion in the horse mode have to be defined in the software to simuation the horse motion in restraints. C. Adding Constraints in the Mode C.. Joint Constraint In this thesis, a joints are modeed as revoute joints aowing two adjacent parts to rotate in the saggita pane. In SoidWorks, these joints can be created by setting concentric and coincident constraints on two parts. Concentric constraint aows the two segments to side aong and to rotate about the z-axis running through the center of the parae and concentric hoes of each part. Coincident constraint aows the two segments to side aong the x-y pane, with the parae sides sharing a common pane. It aso aows the two segments to rotate about the z-axis. Once the revoute joints are defined, joint reaction forces can be obtained from simuation resuts. C.. Hoof Constraint In this thesis, the hooves of the anima are assumed to be fixed to the ground. ixing the horse hooves in the simuation is done by fixing the hooves with a ground part as shown in igure C.. 96

113 The fixing constraint is created with smart faster function in SoidWorks. The hoof has no DO with this constraint and the effect is simiar to naiing the hoof to the ground. igure C.: Modeing of hoof restraint C..3 Upper Arm and Trunk Constraint The upper arm and trunk of the horse is assumed to be constrained in a way that ony vertica movement is aowed. In the simuation, this is set with a siding joint between the upper arm and a ground part as shown in igure C.. Horizonta movement of the upper arm and trunk is not aowed with this constraint. Upper arm Ground part igure C.: Setting the transationa constraint at the upper arm 97

114 C..4 Lower Leg Restraint Besides the hoof restraint, restraints on ower egs are required to immobiize the whoe eg. These restraints can be modeed as a cabe tightening the eg with the ground. Springs with high stiffness assumed at 30,000N/mm is added to the system to simuate the cabes. Spring forces required to hod eg firmy are obtained as simuation resuts. C. Appying Musce orce Musce forces in the eg are simuated as action-ony forces appying on the eg. They are assumed to be constant force during the fighting period. The action ine of the musce force change as the egs rotate. This effect is created with two force direction reference bars in the mode as shown in igure C.3, an exampe of modeing the biceps musce force. One bar rotates around the origin of the biceps and the other rotates around the insertion point. Their ong edges are set to aign during the rotation. The ine between the insertion and origin of the biceps indicates force direction regardess of rotation.this edge aways indicates the straight ine between musce origin and insertion regardess of the rotation. The biceps force direction is set to foow the direction of this ine. igure C.3: Setting the biceps musce force 98

115 C.3 Initia Veocity and Acceeration As described in the thesis, when anayzing the dynamic jerking effect, the jerking is divided into severa phases. The initia veocity and /or acceeration may be required to describe the motion. These initia conditions are input of the simuation program and can be given through motion properties page in Cosmos. Refer to the Cosmos hep document for more information about setting the motion properties for the system. C.4 Body Resistance to Motion Severa things in the skeeta muscuar system may resist the dynamic motion and in turn reduce the breaking force generated in dynamic jerking. Athough it is hard to evauate their infuence in the system, incuding these resistances in the mode is necessary to avoid egs member move with unreaisticay high acceerations in the simuation. Spring eements are introduced to represent the body resistance. Springs are oaded with initia compression force (3,000 N for foreimb and 5,000N for hindimb, igure C.4) to simuate the initia resistance. Then as the egs move up, more resistance wi be generated from the spring eements (stiffness of the springs are 30N/mm for foreimbs and 0N/mm for hindimbs). The settings for the spring eements ensure that the mass on top of the imbs can move with acceeration between g-3g, and eg members can have enough energy to be pued to the highest eve permitted by the range of motion during the dynamic jerking. 99

116 igure C.4: Simuating body resistance to the motion 00