Constraint and Singularity Analysis of the Exechon Tripod

The paper discusses mobility and singularities of the Exe- chon three-degree-of-freedom (dof) parallel mechanism (PM) on which a family of parallel kinematic machines is based. Exe- chon designs are used by a number of machine-Tool makers. A new version of the manipulator has been developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. The PM has two UPR (4-dof) legs, con- strained to move in a common rotating plane, and an SPR (5-dof) leg. The paper focuses on the constraint and singularity analysis of the mechanism. The screw systems of end-effector freedoms and constraints are identified. The singular configurations are classified in detail and their geometric interpretation is discussed. The velocity kinematics and the Jacobian operator are formulated via a screw-system approach. A fully parameterized package of Maple tools has been developed and used to visualize singularities and their consequences.