This paper presents a planar four-bar approximate motion synthesis technique that uses only pole locations. Synthesis for rigid-body guidance determines the linkage dimensions that guide a body in a desired manner. The desired motion is specified with task positions including a location and orientation angle. Approximation motion synthesis is necessary when an exact match to the task positions cannot be obtained. A linkage that achieves the task positions as closely as possible becomes desired. Structural error refers to the deviations between the task positions and the linkage’s generated positions. A challenge in approximate motion synthesis is that structural error involves metrics that include location and orientation. A best-fit solution is not evident because the structural error is based on an objective function that combines the location and orientation. Such solutions lack bi-invariance because a change in reference for the motion changes the values of the metric. This work uses only displacement poles, described solely by their coordinates, as they sufficiently characterize the relative task positions. The optimization seeks to minimize the distance between the poles of the task positions and the poles of the generated positions. The use of poles results in a bi-invariant statement of the problem.

Full use of the upper limb is necessary to carry out most tasks of daily life. Upper limb deficiencies, whether through complete or incomplete paralysis, inevitably lead to a loss of autonomy. Assistive orthoses are a potential method for restoring some autonomy. Pronation and supination, the turning of the wrist relative to the elbow, receives less focus than other joint movements in the arm. First, the utility of this degree-of-freedom in the arm is less obvious. Second, when compared to flexion and extension of the elbow, wrist prono-supination has no clear center of rotation due to the combined movement of the ulna and the radius bones as they cross and uncross in the forearm. This paper presents initial work in the design of a mechanism for a portable assistive orthosis that is expected to include powered prono-supination. The component proposed in this work is based on a spherical mechanism architecture. The capacity of these mechanisms to have a hollow center and to produce paths that follow arcs on spheres makes them worth consideration in this application. An optimization was carried out to perform path generation of a single spherical four-bar with the intent of replicating it three times to create the device proposed in this work. The mechanical design was modeled and a conceptual prototype was constructed to perform preliminary operational evaluations.