A task-based type synthesis of novel 2T2R parallel mechanisms

• Generic task-based synthesis methodology proposed and exemplified on 2T2R mechanisms.
• Screw theory and concept of motion pattern used to specify a desired mobility.
• Kinematic inversion applied to formulate motion patterns relative to a moving frame.
• Proposal of several novel mechanical architectures for surgical needle manipulation.

This article discusses a generic synthesis methodology using the tools of screw theory and the concept of motion pattern, application of which is illustrated by the synthesis of novel parallel mechanisms suited to the task of needle manipulation derived from a medical application. From the minimal 2T2R mobility required for such task, two different motion patterns are derived and have permitted the synthesis of two novel 2T2R parallel mechanisms. Application of the kinematic inversion principle is demonstrated for special cases where the motion pattern is defined with respect to the moving platform. Throughout the synthesis process, a set of preference rules qualifying the architecture kinematic complexity is utilized in order to obtain parallel mechanisms with reduced complexity. These rules are related to the geometric conditions on the placement of the joint axes within and between the synthesized legs. Each parallel mechanism candidate is tested for conditions of full-cycle mobility. Finally, the selection of actuated joints is validated by analyzing the full direct Jacobian matrix.