Kinematic analysis of a 6R single-loop overconstrained spatial mechanism for circular translation

• Analyzed a 6R overconstrained spatial mechanism for circular translation
• Kinematic analysis was reduced to the solution of a quadratic equation.
• Revealed self-motion of the 6R mechanism.
• The 6R mechanism generally has one or two circuits (closure modes).
• The 6R mechanism generally has 0, 2 or 4 full-turn revolute joints.

This paper deals with the kinematic analysis of a double-spherical 6R and parallelogram 4R based single degree-of-freedom overconstrained 6R spatial mechanism for circular translation (DSPB6RCT). How to construct a DSPB6RCT is recalled first. A closed-form solution to the kinematic analysis of the mechanism is then discussed in detail. The kinematic analysis of the mechanism is reduced to the solution of a univariate quadratic equation. The self-motion of a DSPB6RCT is further investigated. The analysis shows that a DSPB6RCT usually has two solutions to the kinematic analysis for a given input. Numerical examples demonstrate that this class of mechanisms may have 0, 2 or 4 full-turn revolute joints and one or two circuits (closure modes or branches). This work provides a solid starting point for further investigation on the classification and application of DSPB6RCTs as well as the kinematic analysis of other classes of overconstrained 6R spatial mechanisms for circular translation. The results can also be used for the type synthesis and singularity analysis of translational parallel mechanisms.