Displacement Analysis of Spatial Six-Link, 5R-C Mechanisms: A General Solution

Four angular displacement equations are derived for the spatial 5R-C hexagon from which an input-output equation of 16th degree in the tan-half-angle of the output angular displacement for each of the RCRRRR, RRCRRR mechanisms and the yet unsolved RRRRRC² mechanism can be obtained by the elimination of two unwanted variables in a single operation. This novel problem formulation is a general solution for all 5R-C mechanisms. Results are verified by a numerical example.