McGill Dept. of Mechanical Engineering MECH572 Introduction to robotics Lecture 10
MECH572 Introduction To Robotics Lecture 10 Dept. Of Mechanical Engineering
Review Fundamentals of multibody dynamics Newton-Euler equation I;=-×工+n+nF mici=fh Rely on free-body diagram. Constraint force involved Compact form M t i=-WiMti+w+ Working Constraint rench Wrench M;三 IO|,wa≡oO o mi
Review • Fundamentals of Multibody Dynamics Newton-Euler Equation Rely on free-body diagram. Constraint force involved. Compact form: Working Wrench Constraint Wrench
Review Fundamentals of Multibody dynamics Euler-Lagarange Equation d(a0)-80= or d/0L\_aL=pn d/at aT d(6/-80 L≡T-V Kinetic energy T=∑=∑M41=M= atTu In terms of twist T=50 I(0)0 In terms of generalized coordinates and inertia Alternative form ofE-L equation I+(b-1[ab+a=中n
Review • Fundamentals of Multibody Dynamics Euler-Lagarange Equation Kinetic energy: Alternative form of E-L equation or In terms of twist In terms of generalized coordinates and inertia
Review Fundamentals of multibody dynamics Summary Newton-Euler Equation Element(body ) level formulation All forces/moments involved(active, constraints,.) Reference point -mass centre Euler-Lagarange Equation System level formulation System kinetic/potential energy involved Generalized coordinates
Review • Fundamentals of Multibody Dynamics Summary: Newton-Euler Equation - Element (body) level formulation - All forces/moments involved (active, constraints,…) - Reference point – mass centre Euler-Lagarange Equation - System level formulation - System kinetic/potential energy involved - Generalized coordinates
Inverse Dynamics Overview of Recursive Algorithm Inverse Dynamics: Known time history of joint position, rate and acceleration, compute joint torque Recursive algorithm: The problem is formulated as a recursive process in such a way that the computation can be proceed from one link to the next Z Kinematics Computation 0,0 ,,b,.0 Cc Dynamics Computation
Y Z 1 1 1 , , 2 2 2 , , n n n , , … 1 1 c , c 2 2 c , c 3 3 c , c 1 1 ω ,ω 2 2 ω ,ω 3 3 ω ,ω Kinematics Computation Dynamics Computation f Inverse Dynamics • Overview of Recursive Algorithm Inverse Dynamics: Known time history of joint position, rate and acceleration, compute joint torque Recursive Algorithm: The problem is formulated as a recursive process in such a way that the computation can be proceed from one link to the next. X n