ourse topics Introduction Mathematical Background Rigid- Body Mechanics Robotic Kinematics Robotic dynamics

Review Rigid-body rotation -Representations Representat Matrix Linear Invariant Quadratic Invariant Natural Invariant on (Euler Parameters)

Midterm Exam Date&Time:19:00-21:00Oct25.2004 Open book Chapters 2 3 of the text book Note: Regular lecture will take place 18: 00-18: 45 on Oct 25

Review Robot Kinematics Geometric Anal ysis x=f(0) of Differential analysis 0 Forward(direct)vs Inverse Kinematics problem Inverse Kinematics Problem(IKP

Review Velocity, Acceleration and Static Analysis Mapping between Cartesian and joint space Linear transformation 0=t T Joint rate -+ Cartesian rate EE Wrench→→ Joint force/torque Rate anal ysis Static anal ysis

Review Basic robotic Kinematic problems Direct(forward) Kinematics Inverse Kinematics · DH Notation

Review Concept of Screw Motion of a rigid body

Review Overview of fields of robotics Concept of vector Space and linear transformation Ax = b linear system of equation mXn n m Column Space(range ), Null space Properties: A(ax+By)=aAX+ BAy Useful linear Transformation in 3-dimensional space

Review Fundamentals of multibody dynamics Newton-Euler equation I;=-×工+n+nF =fw+ff Rely on free-body diagram. Constraint force involved Compact form m ti=-WiMti+w+wf

Review Recursive Inverse dynamics Inverse Dvnamics-Known joint angles o> compute joint torques 1)Outward Recursion -Kinematic Computation Known 0.0.0 Compute t, From 0 to n, recursively based on geometrical and differential relationship associated with each link