Manipulator Dynamics 2. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA
|
|
- Arabella Cooper
- 5 years ago
- Views:
Transcription
1 Manipulator Dynamics 2
2 Forward Dynamics Problem Given: Joint torques and links geometry, mass, inertia, friction Compute: Angular acceleration of the links (solve differential equations) Solution Dynamic Equations - Newton-Euler method or Lagrangian Dynamics τ M( ) V(, ) G( ) F(, )
3 Inverse Dynamics Problem Given: Angular acceleration, velocity and angels of the links in addition to the links geometry, mass, inertia, friction Compute: Joint torques Solution Dynamic Equations - Newton-Euler method or Lagrangian Dynamics τ M( ) V(, ) G( ) F(, )
4 Dynamics - Newton-Euler Equations To solve the Newton and Euler equations, we ll need to develop mathematical terms for: v c c I F N The linear acceleration of the center of mass The angular acceleration The Inertia tensor (moment of inertia) - The sum of all the forces applied on the center of mass - The sum of all the moments applied on the center of mass F mv c c c N I I
5 Iterative Newton-Euler Equations - Solution Procedure Step 1 - Calculate the link velocities and accelerations iteratively from the robot s base to the end effector Step 2 - Write the Newton and Euler equations for each link.
6 Iterative Newton-Euler Equations - Solution Procedure Step 3 - Use the forces and torques generated by interacting with the environment (that is, tools, work stations, parts etc.) in calculating the joint torques from the end effector to the robot s base.
7 Iterative Newton-Euler Equations - Solution Procedure Error Checking - Check the units of each term in the resulting equations v g Gravity Effect - The effect of gravity can be included by setting 0. This is the equivalent to saying that the base of the robot is accelerating upward at 1 g. The result of this accelerating is the same as accelerating all the links individually as gravity does. 0
8 Moment of Inertia / Inertia Tensor
9 Moment of Inertia Intuitive Understanding F mv c c c N I I
10 Moment of Inertia Intuitive Understanding
11 Moment of Inertia Intuitive Understanding
12 Moment of Inertia Intuitive Understanding
13 Moment of Inertia Particle WRT Axis
14 Moment of Inertia Solid WRT Axis
15 Moment of Inertia Solid WRT Frame
16 Moment of Inertia Solid WRT an Arbitrary Axis
17 Moment of Inertia Solid WRT an Arbitrary Axis
18 Moment of Inertia Solid WRT an Arbitrary Axis For a rigid body that is free to move in a 3D space there are infinite possible rotation axes The intertie tensor characterizes the mass distribution of the rigid body with respect to a specific coordinate system
19 Inertia Tensor For a rigid body that is free to move in a 3D space there are infinite possible rotation axes The intertie tensor characterizes the mass distribution of the rigid body with respect to a specific coordinate system The intertie Tensor relative to frame {A} is express as a matrix A I Ixx Ixy Ixz Ixy Iyy Iyz Ixz Iyz Izz
20 Inertia Tensor A I Ixx Ixy Ixz Ixy Iyy Iyz Ixz Iyz Izz I I I xx yy zz V V V ( y ( x ( x z z y ) dv ) d M assmoments of ) d inertia I I I xy xz yz V V V xyd xzd M assproductsof yzd inertia
21 Tensor of Inertia Example This set of six independent quantities for a given body, depend on the position and orientation of the frame in which they are defined We are free to choose the orientation of the reference frame. It is possible to cause the product of inertia to be zero I I I xy xz yz A I Ixx Ixy Ixz 0 0 M assproductsof inertia 0 Ixy Iyz Ixx 0 0 The axes of the reference frame when so aligned are called the principle axes and the corresponding mass moments are called the principle moments of intertie Iyy Iyy A I Ixz Iyz Izz Izz
22 Tensor of Inertia Example
23 Tensor of Inertia Example
24 Parallel Axis Theorem 1D The inertia tensor is a function of the position and orientation of the reference frame Parallel Axis Theorem How the inertia tensor changes under translation of the reference coordinate system
25 Parallel Axis Theorem 3D
26 Parallel Axis Theorem 3D
27 Inertia Tensor
28 Tensor of Inertia Example
29 Rotation of the Inertia Tensor Given: The inertia tensor of the a body expressed in frame A Frame B is rotate with respect to frame A Find The inertia tensor of frame B The angular Momentum of a rigid body rotating about an axis passing through is H A I A Let s transform the angular momentum vector to frame B A H B A B RH A
30
31
32 Inertia Tensor 2/ The elements for relatively simple shapes can be solved from the equations describing the shape of the links and their density. However, most robot arms are far from simple shapes and as a result, these terms are simply measured in practice.
33 Inertia Tensor 2/
34 Inertia Tensor 2/
35
36
37
38
39
40
41
42
43
Artificial Intelligence & Neuro Cognitive Systems Fakultät für Informatik. Robot Dynamics. Dr.-Ing. John Nassour J.
Artificial Intelligence & Neuro Cognitive Systems Fakultät für Informatik Robot Dynamics Dr.-Ing. John Nassour 25.1.218 J.Nassour 1 Introduction Dynamics concerns the motion of bodies Includes Kinematics
More informationIn this section of notes, we look at the calculation of forces and torques for a manipulator in two settings:
Introduction Up to this point we have considered only the kinematics of a manipulator. That is, only the specification of motion without regard to the forces and torques required to cause motion In this
More informationManipulator Dynamics (1) Read Chapter 6
Manipulator Dynamics (1) Read Capter 6 Wat is dynamics? Study te force (torque) required to cause te motion of robots just like engine power required to drive a automobile Most familiar formula: f = ma
More informationCP1 REVISION LECTURE 3 INTRODUCTION TO CLASSICAL MECHANICS. Prof. N. Harnew University of Oxford TT 2017
CP1 REVISION LECTURE 3 INTRODUCTION TO CLASSICAL MECHANICS Prof. N. Harnew University of Oxford TT 2017 1 OUTLINE : CP1 REVISION LECTURE 3 : INTRODUCTION TO CLASSICAL MECHANICS 1. Angular velocity and
More informationChapter 6: Momentum Analysis
6-1 Introduction 6-2Newton s Law and Conservation of Momentum 6-3 Choosing a Control Volume 6-4 Forces Acting on a Control Volume 6-5Linear Momentum Equation 6-6 Angular Momentum 6-7 The Second Law of
More informationChapter 6: Momentum Analysis of Flow Systems
Chapter 6: Momentum Analysis of Flow Systems Introduction Fluid flow problems can be analyzed using one of three basic approaches: differential, experimental, and integral (or control volume). In Chap.
More informationDynamics. describe the relationship between the joint actuator torques and the motion of the structure important role for
Dynamics describe the relationship between the joint actuator torques and the motion of the structure important role for simulation of motion (test control strategies) analysis of manipulator structures
More information6. 3D Kinematics DE2-EA 2.1: M4DE. Dr Connor Myant
DE2-EA 2.1: M4DE Dr Connor Myant 6. 3D Kinematics Comments and corrections to connor.myant@imperial.ac.uk Lecture resources may be found on Blackboard and at http://connormyant.com Contents Three-Dimensional
More informationDynamics. 1 Copyright c 2015 Roderic Grupen
Dynamics The branch of physics that treats the action of force on bodies in motion or at rest; kinetics, kinematics, and statics, collectively. Websters dictionary Outline Conservation of Momentum Inertia
More informationGeneral Physics I. Lecture 10: Rolling Motion and Angular Momentum.
General Physics I Lecture 10: Rolling Motion and Angular Momentum Prof. WAN, Xin (万歆) 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Outline Rolling motion of a rigid object: center-of-mass motion
More informationSpacecraft Dynamics and Control
Spacecraft Dynamics and Control Matthew M. Peet Arizona State University Lecture 16: Euler s Equations Attitude Dynamics In this Lecture we will cover: The Problem of Attitude Stabilization Actuators Newton
More informationDynamics. Basilio Bona. Semester 1, DAUIN Politecnico di Torino. B. Bona (DAUIN) Dynamics Semester 1, / 18
Dynamics Basilio Bona DAUIN Politecnico di Torino Semester 1, 2016-17 B. Bona (DAUIN) Dynamics Semester 1, 2016-17 1 / 18 Dynamics Dynamics studies the relations between the 3D space generalized forces
More informationChapter 5. . Dynamics. 5.1 Introduction
Chapter 5. Dynamics 5.1 Introduction The study of manipulator dynamics is essential for both the analysis of performance and the design of robot control. A manipulator is a multilink, highly nonlinear
More information1/30. Rigid Body Rotations. Dave Frank
. 1/3 Rigid Body Rotations Dave Frank A Point Particle and Fundamental Quantities z 2/3 m v ω r y x Angular Velocity v = dr dt = ω r Kinetic Energy K = 1 2 mv2 Momentum p = mv Rigid Bodies We treat a rigid
More informationRigid body simulation. Once we consider an object with spatial extent, particle system simulation is no longer sufficient
Rigid body dynamics Rigid body simulation Once we consider an object with spatial extent, particle system simulation is no longer sufficient Rigid body simulation Unconstrained system no contact Constrained
More informationRotational & Rigid-Body Mechanics. Lectures 3+4
Rotational & Rigid-Body Mechanics Lectures 3+4 Rotational Motion So far: point objects moving through a trajectory. Next: moving actual dimensional objects and rotating them. 2 Circular Motion - Definitions
More informationDynamics. Dynamics of mechanical particle and particle systems (many body systems)
Dynamics Dynamics of mechanical particle and particle systems (many body systems) Newton`s first law: If no net force acts on a body, it will move on a straight line at constant velocity or will stay at
More informationTranslational and Rotational Dynamics!
Translational and Rotational Dynamics Robert Stengel Robotics and Intelligent Systems MAE 345, Princeton University, 217 Copyright 217 by Robert Stengel. All rights reserved. For educational use only.
More informationRotational Motion. Chapter 4. P. J. Grandinetti. Sep. 1, Chem P. J. Grandinetti (Chem. 4300) Rotational Motion Sep.
Rotational Motion Chapter 4 P. J. Grandinetti Chem. 4300 Sep. 1, 2017 P. J. Grandinetti (Chem. 4300) Rotational Motion Sep. 1, 2017 1 / 76 Angular Momentum The angular momentum of a particle with respect
More informationExplicit Lagrangian Formulation of the Dynamic Regressors for Serial Manipulators
Explicit Lagrangian Formulation of the Dynamic Regressors for Serial Manipulators M Gabiccini 1 A Bracci 1 D De Carli M Fredianelli A Bicchi 1 Dipartimento di Ingegneria Meccanica Nucleare e della Produzione
More informationProgramming Project 2: Harmonic Vibrational Frequencies
Programming Project 2: Harmonic Vibrational Frequencies Center for Computational Chemistry University of Georgia Athens, Georgia 30602 Summer 2012 1 Introduction This is the second programming project
More informationRobot Control Basics CS 685
Robot Control Basics CS 685 Control basics Use some concepts from control theory to understand and learn how to control robots Control Theory general field studies control and understanding of behavior
More informationRigid body dynamics. Basilio Bona. DAUIN - Politecnico di Torino. October 2013
Rigid body dynamics Basilio Bona DAUIN - Politecnico di Torino October 2013 Basilio Bona (DAUIN - Politecnico di Torino) Rigid body dynamics October 2013 1 / 16 Multiple point-mass bodies Each mass is
More informationLecture 11 Overview of Flight Dynamics I. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore
Lecture 11 Overview of Flight Dynamics I Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Point Mass Dynamics Dr. Radhakant Padhi Asst. Professor
More informationRigid Body Rotation. Speaker: Xiaolei Chen Advisor: Prof. Xiaolin Li. Department of Applied Mathematics and Statistics Stony Brook University (SUNY)
Rigid Body Rotation Speaker: Xiaolei Chen Advisor: Prof. Xiaolin Li Department of Applied Mathematics and Statistics Stony Brook University (SUNY) Content Introduction Angular Velocity Angular Momentum
More informationIf the symmetry axes of a uniform symmetric body coincide with the coordinate axes, the products of inertia (Ixy etc.
Prof. O. B. Wright, Autumn 007 Mechanics Lecture 9 More on rigid bodies, coupled vibrations Principal axes of the inertia tensor If the symmetry axes of a uniform symmetric body coincide with the coordinate
More informationMultibody simulation
Multibody simulation Dynamics of a multibody system (Euler-Lagrange formulation) Dimitar Dimitrov Örebro University June 16, 2012 Main points covered Euler-Lagrange formulation manipulator inertia matrix
More informationVideo 3.1 Vijay Kumar and Ani Hsieh
Video 3.1 Vijay Kumar and Ani Hsieh Robo3x-1.3 1 Dynamics of Robot Arms Vijay Kumar and Ani Hsieh University of Pennsylvania Robo3x-1.3 2 Lagrange s Equation of Motion Lagrangian Kinetic Energy Potential
More informationRigid bodies - general theory
Rigid bodies - general theory Kinetic Energy: based on FW-26 Consider a system on N particles with all their relative separations fixed: it has 3 translational and 3 rotational degrees of freedom. Motion
More informationLesson Rigid Body Dynamics
Lesson 8 Rigid Body Dynamics Lesson 8 Outline Problem definition and motivations Dynamics of rigid bodies The equation of unconstrained motion (ODE) User and time control Demos / tools / libs Rigid Body
More informationMultibody simulation
Multibody simulation Dynamics of a multibody system (Newton-Euler formulation) Dimitar Dimitrov Örebro University June 8, 2012 Main points covered Newton-Euler formulation forward dynamics inverse dynamics
More informationGeneral Theoretical Concepts Related to Multibody Dynamics
General Theoretical Concepts Related to Multibody Dynamics Before Getting Started Material draws on two main sources Ed Haug s book, available online: http://sbel.wisc.edu/courses/me751/2010/bookhaugpointers.htm
More information(W: 12:05-1:50, 50-N202)
2016 School of Information Technology and Electrical Engineering at the University of Queensland Schedule of Events Week Date Lecture (W: 12:05-1:50, 50-N202) 1 27-Jul Introduction 2 Representing Position
More informationMECH 5312 Solid Mechanics II. Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso
MECH 5312 Solid Mechanics II Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso Table of Contents Preliminary Math Concept of Stress Stress Components Equilibrium
More informationGame Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost
Game and Media Technology Master Program - Utrecht University Dr. Nicolas Pronost Rigid body physics Particle system Most simple instance of a physics system Each object (body) is a particle Each particle
More informationClassical Mechanics. Luis Anchordoqui
1 Rigid Body Motion Inertia Tensor Rotational Kinetic Energy Principal Axes of Rotation Steiner s Theorem Euler s Equations for a Rigid Body Eulerian Angles Review of Fundamental Equations 2 Rigid body
More informationVideo 2.1a Vijay Kumar and Ani Hsieh
Video 2.1a Vijay Kumar and Ani Hsieh Robo3x-1.3 1 Introduction to Lagrangian Mechanics Vijay Kumar and Ani Hsieh University of Pennsylvania Robo3x-1.3 2 Analytical Mechanics Aristotle Galileo Bernoulli
More informationLecture II: Rigid-Body Physics
Rigid-Body Motion Previously: Point dimensionless objects moving through a trajectory. Today: Objects with dimensions, moving as one piece. 2 Rigid-Body Kinematics Objects as sets of points. Relative distances
More informationLecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202)
J = x θ τ = J T F 2018 School of Information Technology and Electrical Engineering at the University of Queensland Lecture Schedule Week Date Lecture (M: 2:05p-3:50, 50-N202) 1 23-Jul Introduction + Representing
More informationPhysical Simulation. October 19, 2005
Physical Simulation October 19, 2005 Objects So now that we have objects, lets make them behave like real objects Want to simulate properties of matter Physical properties (dynamics, kinematics) [today
More informationROTATIONAL MOTION. dv d F m m V v dt dt. i i i cm i
ROTATIONAL MOTION Consder a collecton of partcles, m, located at R relatve to an nertal coordnate system. As before wrte: where R cm locates the center of mass. R Rcm r Wrte Newton s second law for the
More information2.003 Quiz #1 Review
2.003J Spring 2011: Dynamics and Control I Quiz #1 Review Massachusetts Institute of Technology March 5th, 2011 Department of Mechanical Engineering March 6th, 2011 1 Reference Frames 2.003 Quiz #1 Review
More informationDYNAMICS OF SERIAL ROBOTIC MANIPULATORS
DYNAMICS OF SERIAL ROBOTIC MANIPULATORS NOMENCLATURE AND BASIC DEFINITION We consider here a mechanical system composed of r rigid bodies and denote: M i 6x6 inertia dyads of the ith body. Wi 6 x 6 angular-velocity
More informationExercise 1: Inertia moment of a simple pendulum
Exercise : Inertia moment of a simple pendulum A simple pendulum is represented in Figure. Three reference frames are introduced: R is the fixed/inertial RF, with origin in the rotation center and i along
More information3-D Kinetics of Rigid Bodies
3-D Kinetics of Rigid Bodies Angular Momentum Generalized Newton s second law for the motion for a 3-D mass system Moment eqn for 3-D motion will be different than that obtained for plane motion Consider
More informationLecture AC-1. Aircraft Dynamics. Copy right 2003 by Jon at h an H ow
Lecture AC-1 Aircraft Dynamics Copy right 23 by Jon at h an H ow 1 Spring 23 16.61 AC 1 2 Aircraft Dynamics First note that it is possible to develop a very good approximation of a key motion of an aircraft
More informationRigid Body Dynamics and Beyond
Rigid Body Dynamics and Beyond 1 Rigid Bodies 3 A rigid body Collection of particles Distance between any two particles is always constant What types of motions preserve these constraints? Translation,
More informationInstructor (Oussama Khatib)
IntroductionToRobotics-Lecture11 Instructor (Oussama Khatib):All right. Let s get started. So the video segment today is quite interesting. It was presented at the 2000 International Conference on Robotic
More informationPhysics 351, Spring 2018, Homework #9. Due at start of class, Friday, March 30, 2018
Physics 351, Spring 218, Homework #9. Due at start of class, Friday, March 3, 218 Please write your name on the LAST PAGE of your homework submission, so that we don t notice whose paper we re grading
More informationPLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when
More informationKinetics of Spatial Mechanisms: Kinetics Equation
Lecture Note (6): Kinetics of Spatial Mechanisms: Kinetics Equation Objectives - Kinetics equations - Problem solving procedure - Example analysis Kinetics Equation With respect to the center of gravity
More informationRobot Dynamics II: Trajectories & Motion
Robot Dynamics II: Trajectories & Motion Are We There Yet? METR 4202: Advanced Control & Robotics Dr Surya Singh Lecture # 5 August 23, 2013 metr4202@itee.uq.edu.au http://itee.uq.edu.au/~metr4202/ 2013
More informationPart 8: Rigid Body Dynamics
Document that contains homework problems. Comment out the solutions when printing off for students. Part 8: Rigid Body Dynamics Problem 1. Inertia review Find the moment of inertia for a thin uniform rod
More informationDetermination of Locally Varying Directions through Mass Moment of Inertia Tensor
Determination of Locally Varying Directions through Mass Moment of Inertia Tensor R. M. Hassanpour and C.V. Deutsch Centre for Computational Geostatistics Department of Civil and Environmental Engineering
More informationOptimal Control, Guidance and Estimation. Lecture 16. Overview of Flight Dynamics II. Prof. Radhakant Padhi. Prof. Radhakant Padhi
Optimal Control, Guidance and Estimation Lecture 16 Overview of Flight Dynamics II Prof. Radhakant Padhi Dept. of erospace Engineering Indian Institute of Science - Bangalore Point Mass Dynamics Prof.
More informationGeneral Physics (PHY 2130)
General Physics (PHY 130) Lecture 0 Rotational dynamics equilibrium nd Newton s Law for rotational motion rolling Exam II review http://www.physics.wayne.edu/~apetrov/phy130/ Lightning Review Last lecture:
More informationTwo Posts to Fill On School Board
Y Y 9 86 4 4 qz 86 x : ( ) z 7 854 Y x 4 z z x x 4 87 88 Y 5 x q x 8 Y 8 x x : 6 ; : 5 x ; 4 ( z ; ( ) ) x ; z 94 ; x 3 3 3 5 94 ; ; ; ; 3 x : 5 89 q ; ; x ; x ; ; x : ; ; ; ; ; ; 87 47% : () : / : 83
More informationSatellite attitude control system simulator
Shock and Vibration 5 (28) 395 42 395 IOS Press Satellite attitude control system simulator G.T. Conti and L.C.G. Souza National Institute for Space Research, INPE, Av. dos Astronautas 758, 2227-, S ão
More informationLecture Note 12: Dynamics of Open Chains: Lagrangian Formulation
ECE5463: Introduction to Robotics Lecture Note 12: Dynamics of Open Chains: Lagrangian Formulation Prof. Wei Zhang Department of Electrical and Computer Engineering Ohio State University Columbus, Ohio,
More informationDynamics of Open Chains
Chapter 9 Dynamics of Open Chains According to Newton s second law of motion, any change in the velocity of a rigid body is caused by external forces and torques In this chapter we study once again the
More informationChapter 12 Static Equilibrium
Chapter Static Equilibrium. Analysis Model: Rigid Body in Equilibrium. More on the Center of Gravity. Examples of Rigid Objects in Static Equilibrium CHAPTER : STATIC EQUILIBRIUM AND ELASTICITY.) The Conditions
More informationIntroduction to Robotics
J. Zhang, L. Einig 277 / 307 MIN Faculty Department of Informatics Lecture 8 Jianwei Zhang, Lasse Einig [zhang, einig]@informatik.uni-hamburg.de University of Hamburg Faculty of Mathematics, Informatics
More informationChapter 4 The Equations of Motion
Chapter 4 The Equations of Motion Flight Mechanics and Control AEM 4303 Bérénice Mettler University of Minnesota Feb. 20-27, 2013 (v. 2/26/13) Bérénice Mettler (University of Minnesota) Chapter 4 The Equations
More informationChapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
More informationGeneral Definition of Torque, final. Lever Arm. General Definition of Torque 7/29/2010. Units of Chapter 10
Units of Chapter 10 Determining Moments of Inertia Rotational Kinetic Energy Rotational Plus Translational Motion; Rolling Why Does a Rolling Sphere Slow Down? General Definition of Torque, final Taking
More informationTorque and Rotation Lecture 7
Torque and Rotation Lecture 7 ˆ In this lecture we finally move beyond a simple particle in our mechanical analysis of motion. ˆ Now we consider the so-called rigid body. Essentially, a particle with extension
More informationPhysics A - PHY 2048C
Physics A - PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment
More informationExample: Inverted pendulum on cart
Chapter 25 Eample: Inverted pendulum on cart The figure to the right shows a rigid body attached by an frictionless pin (revolute joint to a cart (modeled as a particle. Thecart slides on a horizontal
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
More information7.4 Rigid body simulation*
7.4 Rigid body simulation* Quaternions vs. Rotation Matrices - unit quaternions, a better way to represent the orientation of a rigid body. Why? (1) More compact: 4 numbers vs. 9 numbers (2) Smooth transition
More informationAn experimental robot load identification method for industrial application
An experimental robot load identification method for industrial application Jan Swevers 1, Birgit Naumer 2, Stefan Pieters 2, Erika Biber 2, Walter Verdonck 1, and Joris De Schutter 1 1 Katholieke Universiteit
More informationENGG 5402 Course Project: Simulation of PUMA 560 Manipulator
ENGG 542 Course Project: Simulation of PUMA 56 Manipulator ZHENG Fan, 115551778 mrzhengfan@gmail.com April 5, 215. Preface This project is to derive programs for simulation of inverse dynamics and control
More informationIII. Work and Energy
Rotation I. Kinematics - Angular analogs II. III. IV. Dynamics - Torque and Rotational Inertia Work and Energy Angular Momentum - Bodies and particles V. Elliptical Orbits The student will be able to:
More informationChapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
More informationPSE Game Physics. Session (6) Angular momentum, microcollisions, damping. Oliver Meister, Roland Wittmann
PSE Game Physics Session (6) Angular momentum, microcollisions, damping Oliver Meister, Roland Wittmann 23.05.2014 Session (6)Angular momentum, microcollisions, damping, 23.05.2014 1 Outline Angular momentum
More information112 Dynamics. Example 5-3
112 Dynamics Gravity Joint 1 Figure 6-7: Remotely driven two d.o.r. planar manipulator. Note that, since no external force acts on the endpoint, the generalized forces coincide with the joint torques,
More information(Refer Slide Time: 0:36)
Engineering Mechanics Professor Manoj K Harbola Department of Physics Indian Institute of Technology Kanpur Module 04 Lecture No 35 Properties of plane surfaces VI: Parallel axis transfer theorem for second
More informationAssignment 4: Rigid Body Dynamics
Assignment 4: Rigid Body Dynamics Due April 4 at :59pm Introduction Rigid bodies are a fundamental element of many physical simulations, and the physics underlying their motions are well-understood. In
More informationPhys 7221 Homework # 8
Phys 71 Homework # 8 Gabriela González November 15, 6 Derivation 5-6: Torque free symmetric top In a torque free, symmetric top, with I x = I y = I, the angular velocity vector ω in body coordinates with
More informationChapters 10 & 11: Rotational Dynamics Thursday March 8 th
Chapters 10 & 11: Rotational Dynamics Thursday March 8 th Review of rotational kinematics equations Review and more on rotational inertia Rolling motion as rotation and translation Rotational kinetic energy
More information16. Rotational Dynamics
6. Rotational Dynamics A Overview In this unit we will address examples that combine both translational and rotational motion. We will find that we will need both Newton s second law and the rotational
More informationIn this section, mathematical description of the motion of fluid elements moving in a flow field is
Jun. 05, 015 Chapter 6. Differential Analysis of Fluid Flow 6.1 Fluid Element Kinematics In this section, mathematical description of the motion of fluid elements moving in a flow field is given. A small
More informationThursday Simulation & Unity
Rigid Bodies Simulation Homework Build a particle system based either on F=ma or procedural simulation Examples: Smoke, Fire, Water, Wind, Leaves, Cloth, Magnets, Flocks, Fish, Insects, Crowds, etc. Simulate
More informationApplication of Forces. Chapter Eight. Torque. Force vs. Torque. Torque, cont. Direction of Torque 4/7/2015
Raymond A. Serway Chris Vuille Chapter Eight Rotational Equilibrium and Rotational Dynamics Application of Forces The point of application of a force is important This was ignored in treating objects as
More informationCenter of Gravity Pearson Education, Inc.
Center of Gravity = The center of gravity position is at a place where the torque from one end of the object is balanced by the torque of the other end and therefore there is NO rotation. Fulcrum Point
More information2.003J Spring 2011: Dynamics and Control I On Notation Massachusetts Institute of Technology Department of Mechanical Engineering Feb.
2.J Spring 211: Dynamics and Control I On Notation Department of Mechanical Engineering Feb. 8, 211 On Notation Much of 2.j involves defining then manipulating points, frames of reference, and vectors.
More informationLecture «Robot Dynamics»: Dynamics and Control
Lecture «Robot Dynamics»: Dynamics and Control 151-0851-00 V lecture: CAB G11 Tuesday 10:15 12:00, every week exercise: HG E1.2 Wednesday 8:15 10:00, according to schedule (about every 2nd week) Marco
More informationLeonhard Euler ( September 1783)
LEONHARD EULER (1707 - SEPTEMBER 1783) Leonhard Euler (1707 - September 1783) BEYOND EQUATIONS Leonhard Euler was born in Basle, Switzerland; he was in fact a born mathematician, who went on to become
More informationRobotics. Dynamics. Marc Toussaint U Stuttgart
Robotics Dynamics 1D point mass, damping & oscillation, PID, dynamics of mechanical systems, Euler-Lagrange equation, Newton-Euler recursion, general robot dynamics, joint space control, reference trajectory
More informationNotes on Torque. We ve seen that if we define torque as rfsinθ, and the N 2. i i
Notes on Torque We ve seen that if we define torque as rfsinθ, and the moment of inertia as N, we end up with an equation mr i= 1 that looks just like Newton s Second Law There is a crucial difference,
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1 Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related 2 Torque The door is free to rotate
More informationMANY BILLS OF CONCERN TO PUBLIC
- 6 8 9-6 8 9 6 9 XXX 4 > -? - 8 9 x 4 z ) - -! x - x - - X - - - - - x 00 - - - - - x z - - - x x - x - - - - - ) x - - - - - - 0 > - 000-90 - - 4 0 x 00 - -? z 8 & x - - 8? > 9 - - - - 64 49 9 x - -
More information(Refer Slide Time: 1:58 min)
Applied Mechanics Prof. R. K. Mittal Department of Applied Mechanics Indian Institution of Technology, Delhi Lecture No. # 13 Moments and Products of Inertia (Contd.) Today s lecture is lecture thirteen
More informationEngineering Mechanics
2019 MPROVEMENT Mechanical Engineering Engineering Mechanics Answer Key of Objective & Conventional Questions 1 System of forces, Centoriod, MOI 1. (c) 2. (b) 3. (a) 4. (c) 5. (b) 6. (c) 7. (b) 8. (b)
More informationRotational Motion, Torque, Angular Acceleration, and Moment of Inertia. 8.01t Nov 3, 2004
Rotational Motion, Torque, Angular Acceleration, and Moment of Inertia 8.01t Nov 3, 2004 Rotation and Translation of Rigid Body Motion of a thrown object Translational Motion of the Center of Mass Total
More informationChapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
More informationRobot Dynamics - Rotary Wing UAS: Control of a Quadrotor
Robot Dynamics Rotary Wing AS: Control of a Quadrotor 5-85- V Marco Hutter, Roland Siegwart and Thomas Stastny Robot Dynamics - Rotary Wing AS: Control of a Quadrotor 7..6 Contents Rotary Wing AS. Introduction
More informationChapter 8. Rotational Motion
Chapter 8 Rotational Motion The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of
More informationA DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any
Y Y Y X X «/ YY Y Y ««Y x ) & \ & & } # Y \#$& / Y Y X» \\ / X X X x & Y Y X «q «z \x» = q Y # % \ & [ & Z \ & { + % ) / / «q zy» / & / / / & x x X / % % ) Y x X Y $ Z % Y Y x x } / % «] «] # z» & Y X»
More information