A closed-form solution to the direct kinematics of nearly general parallel manipulators with optimally located three linear extra sensors

This paper presents a new closed-form solution of the direct kinematic problem of nearly general parallel manipulators by using three linear extra sensors. The sensors are disposed at optimal location, connecting the planar base and the planar mobile platform at distinct points. The basic idea is to use the coordinates of the three distinct anchor points of the extra sensors on the mobile platform to represent the pose of the mobile platform. Thus, the extra sensory data enable to reduce the problem to the solution of a system of six linear equations in six of the nine generalized coordinates. The other three coordinates are obtained directly from the extra sensory data. In addition, optimal location of the extra sensors is sought by minimizing the condition number of the linear equations for the least sensitivity to sensor measurement errors. A numerical example is presented for optimal sensor location and the error behavior of the proposed solution scheme by computer simulation.