Geometric construction and kinematic analysis of a 6R single-loop overconstrained spatial mechanism that has three pairs of revolute joints with intersecting joint axes

This paper deals with the geometric construction and kinematic analysis of a single degree-of-freedom 6R overconstrained spatial mechanism (6R mechanism for short) that has three pairs of revolute (R) joints with intersecting joint axes. How to construct a 6R with three pairs of R joints with intersecting joint axes is presented first. The kinematic analysis of the 6R mechanism is then discussed. The analysis shows that the 6R usually has two solutions to the kinematic analysis for a given input. In two configurations in each circuit of the 6R mechanism, the axes of four R joints are coplanar, and the axes of the other two R joints are perpendicular to the plane defined by the above four R joints.