Forward Positional Analysis for the General 4–6 In-Parallel Platform

Abstract

Presented is the forward positional (kinematic) solution for the general case of the 4–6 in-parallel platform mechanism; in particular, the spherical joints of the moving and base platforms are not restricted to lie in planes, but can be freely chosen. The forward positional analysis consists of 13 equations which are reduced to a single thirty-second order polynomial equation in one unknown variable. This new equation is numerically solved and validated by substituting the 32 roots into the 13 forward positional equations. The new analysis is also used to solve an example, with a set of known results from a previously published paper, in which a special case of the 4–6 in-parallel platform is considered; the results are in exact agreement. For a number of general platform and actuator inputs a maximum of 24 real solutions have been found. One example is illustrated.