SYNTHESIS OF A 3-RPS PARALLEL MANIPULATOR BASED ON AXODES

A spatial displacement of a rigid body can be described as a combination of translation and rotation about an axis, known as Instantaneous Screw Axis (ISA). As the rigid body moves over time, ISA will form a ruled surface called axodes. The position and orientation of ISA and its trajectory over time plays an important role to determine kinematic models of the human body. It helps to design wearable orthoses and even to diagnose any pathological patterns. On the other hand, the motion of a rigid body can also be described by a transformation matrix and its time-derivative. This paper presents a synthesis of wearable orthoses based on ISA. The approach is developed based on the relation between two velocity matrices, one computed from the trajectory of the ISA, another one computed from the time-derivative of the transformation matrix. This relation yields a numerical synthesis of parameters of translations and rotations, and design parameters of a rigid body. The developed methodology is applied to a 3-RPS parallel manipulator to obtain parameters of translations and rotations, and platform dimensions for a given set of ISA. The surface of ISA axodes is visualized and three lines of ISA are selected. The poses of a 3-RPS parallel manipulator to achieve the motion defined by a given set of ISA are illustrated. The advantage of this approach is less parameters to be handled, since it aims to synthesize parameters of translations and rotations, instead of coordinates of points. A coupled motion (parasitic motion) undergone by a parallel manipulator can be easily solved by this approach.