Forward Kinematics Analysis of 2RUS/RRS Parallel Mechanism

The iterative search method（ Newton or Quasi-Newton） is an important numerical method for solving the forward kinematics（ FK） problem of parallel mechanisms. Due to the extremely displacement singularity in the limbs,the search space is easy to be out of the mechanism workspace,which causes failed in solving the FK problem of the class of 2 RUS/2 RRS mechanism. Taking the plane series branch as an example,the equivalent method of eliminating the extremely displacement singularity is given,and the 2 RUS/2 RRS mechanism is equivalent to a 2 UPS/2 RPS mechanism. Based on the relationship between the angular velocity and the Euler’s derivative,the 4 × 4 Jacobian matrix is gotten through the virtual mechanism method. The Jacobian matrix of the initial pose of the equivalent mechanism can be taken as the approximate initial value of the Quasi-Newton method,which can reduce the calculation and improve the computational efficiency. The FK problem of 2 RUS/2 RRS are numerically verified by inverse Broyden algorithm in Quasi-Newton method.