Position Analysis of a 3-spr Parallel Mechanism

This paper deals with closed form solutions for the inverse and forward position analyses of a 3-SPR parallel mechanism, which can be used to form the main body of a 5-DOF hybrid robot manipulator. In the inverse position analysis, a fourth order polynomial equation has been formulated, leading to four set of solutions of limb lengths for a given position of the reference point on the platform. In the forward position analysis, a sixteenth order polynomial equation has been derived, leading to four sets of mirror poses given a set of limb lengths. Consequently, the complete sets of solutions for the inverse and forward position analyses of the mechanism have been achieved. An example is given to illustrate the effectiveness of this approach.