An Analytical Method to Find Workspace of a Robotic Manipulator

The workspace of a Robot is determined by an analytical method. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation for serial kinematic chains. This method is based upon analytical criteria for determining singular behavior of the mechanism. By manipulating the Jacobian of the robot by the row rank deficiency condition, the singularities are computed. Then these singularities are substituted into the constraint equations to parameterize singular surfaces. The boundary conditions of the joints are substituted to obtain the other set of singularities. These singularities are substituted in the wrist vector to obtain the range of motion of the robot wrist in three dimensional space, which is the workspace of the Robot. These singularities are plotted in Matlab to develop all the surfaces enveloping the workspace of the Robot. The priactical examples of RV-M1 MITSIBUSHI ROBOT and 3 DOF spatial manipulator are treated with this method.