Forward kinematics analysis of parallel mechanisms with restricted workspace

The iterative search method (Newton-Raphson or Quasi-Newton) is an important numerical method for solving the forward kinematics problem of parallel mechanisms. But there may be a failure when the iterative search method solves the forward kinematics problems of a class of mechanisms, whose workspace is restricted. The extreme displacement singularity in the limbs is one reason for the workspace restriction. An equivalent method is proposed to remove the extremely displacement singularity in the limbs, and the forward kinematics solutions of two representative 6 degree of freedom mechanisms are given to illustrate the mechanism equivalence. For the coupled fewer degree of freedom mechanisms, the coupled motion is another reason for the workspace restriction. The virtual mechanism method and modified Jacobian matrix method are applied to solve the forward kinematics problems of this class of mechanisms. Numerical examples are given to validate the theories proposed above.