Static forces and torques in mechanisms with plane joints, with application to the Tracta coupling

The force and torque components acting on revolute and plane joints are partitioned in a novel way so that the equations of static equilibrium can be written in a standard form, applicable to a single-loop mechanism with any number of links and any kinds of joints, with particular attention given to the plane joint which consists of two flat surfaces held in contact to permit one rotational and two translational degrees of freedom. The analysis utilizes the 3 × 3 dual-number coordinate-transformation matrix to model joints and links and expresses force and torque as a two-component dual force, which formulates the results in a compact form amenable for object-oriented programming to calculate the static loads. Particular attention is given to the Tracta coupling, an RRERR mechanism (rotation-rotation-plane-rotation-rotation joints) which has been used as a constant-velocity shaft coupling and features a plane joint. The formulation allows force and torque components to be expressed so to correspond to displacements specified with respect to the axes of intermediate coordinate frames in the modelling of a plane joint.