A simple new closed-form solution of the direct kinematics of parallel manipulators using three linear extra sensors

Presents a simple closed-form solution of the direct kinematics problem of general parallel manipulators, by using three linear extra sensors. The sensors are disposed in a most general way, connecting the planar base and the planar mobile platform at distinct points. The basic idea is to use the coordinates of the three distinct attachment points of the extra sensors on the mobile platform to represent the posture of the mobile platform. Thus, the extra sensory data enables us to reduce the problem to the solution of a system of 6 linear equations in 6 of the 9 generalized coordinates. The other 3 coordinates are obtained directly from the extra sensory data