Kinematic synthesis using tree topologies

• Dimensional synthesis is developed for articulated systems with a tree topology.
• Rooted tree graphs: articulated systems with several branches and end-effectors.
• Conditions for solvability of the rooted tree graph for a finite-position task.
• Synthesis equations are written in a systematic way for the kinematic task.
• The proposed synthesis methodology is applied for the design of robotic hands.

This paper presents a methodology for the description and finite-position dimensional synthesis of articulated systems with multiple end-effectors. The articulated system is represented as a rooted tree graph. Graph and dimensional synthesis theories are applied to determine when exact finite-position synthesis can be performed on the tree structures by considering the motion for all the possible subgraphs. Several examples of tree topologies are presented and synthesized. This theory has an immediate application on the design of novel multi-fingered hands.