Velocity Kinematics

Abstract

Velocity analysis of a robot is divided into forward and inverse velocity kinematics. Having the time rate of joint variables and calculating the Cartesian velocity of end-effector in the global coordinate frame is the forward velocity kinematics. Determination of the time rate of joint variables based on velocity of end-effector is the inverse velocity kinematics.

Each link of a serial robot has an angular and a translational velocity. The angular velocity of link (i) in the global coordinate frame can be found as a summation of the global angular velocities of its lower links. The velocity kinematics of a robot is defined by the relationship between joint speeds and Cartesian velocity of the end-effector. The coefficient matrix between them is called the Jacobian matrix J. Having J, we are able to find the end-effector speeds for a given set of joint speeds and vice versa. Jacobian is a function of joint coordinates and is the main tool in velocity kinematics of robots. We practically calculate J by Jacobian generating vectors.