Velocity Kinematics and Statics

Table of Contents

Manipulator Jacobian

Minimum Coordinate Forward Kinematics

Just represent the minimum degrees of freedom as coordinates, since we know the # of actuators. Use the minimum set of coordinates to represent location of end effector.

Taking the $\ddot x$, so that we get xdot = df/d\theta * theta_dot, where f/d\theta is the Jacobian.

A configuration of a robot is singular if its Jacobian matrix loses rank -> e-e motion capability becomes zero in one or more directions, e-e can resist infinite force in one or more directions. Product of two areas of motion and force ellispoid is constant.

Geometric Representation of Forward Kinematics

• Space Jacobian V_s = J_s(\theta)\theta_dot, where Js1 = S1, Jsi(\theta) Ad_e(,,,)

• Body Jacobian …