Kinematics and Jacobian analysis of a 6UPS Stewart-Gough platform

In this paper a complete kinematics analysis of a 6UPS Stewart-Gough platform is performed. A new methodology to deal with the forward kinematics problem based on a multibody formulation and a numerical method is presented, resulting in a highly efficient formulation approach. The idea of a multibody formulation is basically to built for each joint that links the body of the robot, a set of equations that define the constraints on their movement so that the joint variables are included in these equations. Once the constraint function is defined, we may use a numerical method to find the kinematic solution. In order to avoid the problem reported with the orientation (Euler's Angles) of the moving platform, a generalized coordinates vector using quaternions is applied. Then, the Jacobian analysis using reciprocal screw systems is described and the workspace is determined. Finally, a design of a simulator using MATLAB as programming tool is presented.