Dimensioning a Constrained Parallel Robot to Reach a Set of Task Positions

The paper considers the problem of setting the dimensions of a system of constrained parallel robots to ensure that together they can position an end-effector in a specified set of positions. The focus is on five degree-of-freedom serial chains that provide point contact, modelled as a spherical joint, with the end-effector. We identify seven such chains which can be used to form 756 parallel robots ranging from one to three degrees of freedom. The algebraic equations of the surfaces that contain the center of the spherical joint of these seven chains can be used to form the design equations for the parallel system. These equations are solved to determine some or all of the structural parameters depending upon the required number of task positions. We demonstrate this by computing the dimensions of a symmetric 3CS parallel robot such that it guides the end-effector through three arbitrarily defined task positions.