MODELING OF A BIOMECHATRONIC MODULE FOR WALK SIMULATION *

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Derek Byrd
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1 11 th National Congress on Theoretical and Applied Mechanics, 2-5 Sept. 2009, Borovets, Bulgaria MODELING OF A BIOMECHATRONIC MODULE FOR WALK SIMULATION * I. CHAVDAROV Central Laboratory of Mechatronics, Bulgarian Academy of Sciences Acad.G. Bonchev str., bl.1, 1113 Sofia, Bulgaria ivan_chavdarov@dir.bg K. DELCHEV, L. ILIEVA-MITUTSOVA, V.VITKOV Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 4, 1113 Sofia kamen@imbm.bas.bg; lidia@imbm.bas.bg ABSTRACT. A virtual prototype of a mechanical module of a biomechatronic system is developed, and the system is used for locomotor rehabilitation of patients-paraplegics. Module mechanics, actuation and control should realize patient s foot loading similar to that during normal walk. The report presents a synthesis of force control of the module step motors that apply respective foot loading, considering the dynamical characteristic of normal walk.modeling and simulation assist the prototype successful realization. KEY WORDS: biomechantronic module; modeling, walk simulation. 1. Introduction A virtual prototype of a mechanical module is developed. It is a unit of a biomechatronic system used for the locomotor rehabilitation of patients-paraplegics. The task is to imitate walking conditions close to normal walk and attend a patient having undergone a severe trauma. Thus, the rehabilitation of spinal cord locomtor capabilities and functioning of man s support-locomotor system can be stimulated maintaining the information flux coming from foot receptors [1]. Module mechanics, actuation and control provide patient s foot loading similar to that of normal walk. A plot of the vertical support reaction in a single-support phase of normal walk is used as a standard (Fig.1). Velocity and the maximal value of foot loading are parameters subject to regulation. * Financial support: Project Development, modeling and study of a biomechatronic module for walk simulation with application in locomotory rehabilitation, Bulgarian Academy of Sciences

2 I. Chavdarov, K. Delchev, L. Ilieva-Mitutsova, V.Vitkov Fig. 1: A plot of foot vertical support reaction under normal walk M 1 1-st maximum, M 2 2-nd maximum, M 3 minimum, G weight of the investigated individual, Т period of the gait right leg left leg 2. Model of a module for foot loading and receptor activation in walk rhythm Generally, the model consists of: 1 solidly fixed elements (stand); М1 linear motor solidly fixed to the foundation and having a rotating shaft 3; М2 linear motor with a rotating shaft 4 fixed by a hinge to the foundation 1; 2 immovable plate solidly fixed to the foundation 1; 5 movable plate with aperture matrix fixed by hinges to the rotating shafts of the linear motors М1 and М2; 8 tensometric platform between the solidly fixed plates 1 and 2. Patient s foot is arranged on plate 5 by means of heel support 6 and fixing devices 7 (Fig.2). Pins (m x n in number) a, b, c, d, e, f,g and h, are mounted in the movable plate 5 with looseness which enables pin motion along the axis. One pin round end contacts the plane of immovable plate 2, while the other one acts on patient s foot. Distribution step and dimensions of pins are shown in Fig. 3. Movable plate 5 shifts with respect to immovable plate 2, and pins a, b, c, d, e, f, g and h axially displace vertically as a result. Hence, pins change their position with respect to the movable plate 5 and act on a foot solidly fixed to it (Fig.2,b). The force of pin action is balanced by foot elastic response. According to the virtual model proposed, foot elastic properties are imitated by means of a number of linear springs Sa, Sb, Sh acting on pins a, b,.h. Foot pressure thus created is recorded by force-measuring platform 8. Depending on foot size, some pins Р are active - P1 (acting on foo, while others are passive P2 (Fig.3). Besides, the impact of different foot areas on pins is not one and the same (Fig.2. b). Divide foot in 4 areas with different elastic properties and consider corresponding coefficients of relative deformation: 1- heel an area with large rigidity (the coefficient of relative deformation is k rd =7.4 [N/m] in this case); 2- arch an area with small rigidity (the coefficient of relative deformation is k rd =5 [N/m]); 3- front part an area with average rigidity (the coefficient of relative deformation is k rd =6 [N/m] ); 4 fingers areas with large rigidity ( k rd =7.4 [N/m]).

Coefficients of relative deformation k have approximate values. They are experimentally found considering pin maximal displacement (5 mm in this case). a) b) Fig.3.

3 Modeling of a biomechatronic module for walk simulation a) b) Fig.2. Model of a device for foot loading and receptor activation in walk rhythm We assume one and the same damping coefficient c = 15 [kg/s] and linear laws for spring and damping forces. Coefficients of relative deformation k have approximate values. They are experimentally found considering pin maximal displacement (5 mm in this case). a) b) Fig.3. Area with active pins P1 acting on foot and load distribution on foot surface during walk (Areas 1-4). 1. Synthesis of laws of control with respect to power of motors of the walk-simulating module. Considering experiments performed by the employment of the virtual model, we have: (3.1) ( = kfi (, where F i ( is the measured value of foot total loading, which can be registered by the tensometric platform 8 of the mechatronic module, and k is similarity coefficient.

4 I. Chavdarov, K. Delchev, L. Ilieva-Mitutsova, V.Vitkov Fig.4. A program of desired walk loading, corresponding to a single-support period of normal walk F d ( is the force applied by the motors. Similarity coefficient k depends on the structure geometry, only, and it is calculated via: max (3.2) k = max Fi where: max Fi = max Fzad is found from the plot of the vertical support reaction of normal walk (Fig.1). Considering phase 1 with duration t А - t B, motor М1 should apply a force proportional to the specified one, i.e.: 1( = kfzad ( (3.3) 2( = 0 Motor 2 is not active in the interval t [ t А, t B ] and it does not set in motion plate 5. Considering phase 2 with duration t B -t D, motor М1 obeys a linear control similar to displacement control [2], with a proportionality coefficient: k(2max Fzad min Fzad ) (3.4) a = 2( tc tb) According to Fig.5, the second motor operates as follows: (3.5) 2( = kfzad ( 1(, t [ t B, t D ] During phase 3 with duration t D - t E, motor М2 operates, only:` 2( = kfzad ( (3.6) 1( = 0 where t [ t D, t E ] and motor М1 does not operate. 4. Numerical example Simulation of patient s foot loading via the virtual prototype of the specialized mechatronic module is performed. Based on the dynamic characteristics of normal walk (Fig.1) and the control algorithm proposed, we find the program of motor operation control, Table 1.

5 Modeling of a biomechatronic module for walk simulation Table 1. Program of force control of motors M1 and M2. Input Motor control Phase Time Program force Force of motor 1 Force of motor t [s] F [N] F1 [N] F2 [N] Simulation results We find good agreement between the loading program, found on the basis of walk dynamic characteristic and virtual prototype loading (Fig. 6).

I. Chavdarov, K. Delchev, L. Ilieva-Mitutsova, V.Vitkov 400 SUM_F (N) vs. time (s) 300 200 100 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Fig.5. Sum of pin forces as function of time.

The universal microprocessor servo-controllers enable one to perform force control. Hence, simulation of force control on the 3D model is applicable to the real device.

6 I. Chavdarov, K. Delchev, L. Ilieva-Mitutsova, V.Vitkov 400 SUM_F (N) vs. time (s) Fig.5. Sum of pin forces as function of time. Fig.6. Comparison between the specified law of force variation performing the simulation. 5. Conclusion Foot loading is realized on the designed virtual prototype by means of two step motors. The universal microprocessor servo-controllers enable one to perform force control. Hence, simulation of force control on the 3D model is applicable to the real device. Modeling and simulation help to the successful realization of a prototype of a biomechatronic system module, providing normal rhythm to the walk of a patient-paraplegic. R E F E R E N C E S [1] PLATONOV А., L. MITUTSOVA, K. DELCHEV, V. VITKOV, I. CHAVDAROV, V. LATKOVSKI, V. YAROSHEVSKY, O. NIKITIN. Developmen of a Mechatronic System GAITSIM for Biomechanical Rehabilitation of Patients Paraplegics. Engineering mechanics, Vol. 14 (2007), No 4, [2] A. PLATONOV, I. CHAVDAROV, L. ILIEVA-MITUTSOVA, V. VITKOV, K. DELCHEV,V. YAROSHEVSKY, N. SERBENJUK, O. NIKITIN. Developmen and Modeling of a Biomechatronic System for Foot Reseptor Activation of Patients Paraplegics, Engineering Mechanics 2008 Proc. On CD, May, 2008, Svratka, Czech Republic,

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