A complete and general solution to the forward kinematics problem of platform-type robotic manipulators

In this paper a general method is presented, based on the data of three point positions, velocities and accelerations of the end effector, for solving the forward kinematics problem of any platform-type manipulator, including the 6 DOF Stewart Platform. Numerical examples are included to demonstrate the application of the method. It is shown that the equations for the forward position kinematics are highly-nonlinear, however, closed-form solutions to the forward rate kinematics and the forward acceleration kinematics can be obtained by solving a system of linear equations. The advantages of using additional passive joint encoders is also discussed, to simplify the solution of the position kinematics problem, and obtain a one-to-one relation between the actuated joint variables and the end effector configurations