Kinematics of common industrial robots

An approach to finding the solution equations for simple manipulators is described which enhances the well known method of Paul, Renaud, and Stevenson, by explicitly making use of known decouplings in the manipulator kinematics. This reduces the set of acceptable equations from which we obtain relationships for the joint variables. For analyzing the Jacobian, such decoupling is also useful since it manifests itself as a block of zeros, which makes inversion much easier. This zero lock can be used to obtain a concise representation for the forward and inverse Jacobian computations. The decoupling also simplifies the calculations sufficiently to allow us to make good use of a symbolic algebra program (MACSYMA) in obtaining our results. Techniques for using MACSYMA in this way are described. Examples are given for several industrial manipulators.