Study on Jacobian, singularity and kinematics sensitivity of the FUM 3-PSP parallel manipulator

• Presenting a methodology to select the practical operational modes of a 3-PSP robot
• Providing a new general perspective in sensitivity analysis
• Presenting direct/inverse sensitivity analyses for the robot's operational modes
• Presenting sensitivity analysis from both end-user and designer point of views

The Jacobian matrices of a robot are commonly utilized in determining its dynamic behavior, workspace singular regions as well as manipulability and sensitivity analysis. This paper provides a new general perspective in analyzing workspace, singularity and sensitivity analyses. This perspective can aid both end-users and robot designers to assess effect of desired end-effector accuracy on required actuator accuracy as well as effect of selected actuator accuracy on the resulting end-effector accuracy. To do this, a 3-PSP parallel robot with specific architecture is considered. Two operational modes called non-pure translational and coupled mixed type modes are considered and Jacobian matrices are obtained and the inverse and direct relations for velocity and acceleration are derived. A methodology to select the most practical operational modes is represented. Next the three well-known singularities as well as the constraint singularity are investigated. Additionally, notion of inverse kinematics singularity (IKS) is defined and existing IKS loci in workspace for the two operational modes are determined. Finally, for the two operational modes, the direct and inverse sensitivity analyses are investigated by defining concept of direct and inverse squared Jacobian matrices. In the direct sensitivity analysis, influence of actuator errors on the position and orientation errors of the moving platform (MP) is determined. In the inverse sensitivity analysis, the allowable actuator error boundaries are determined with respect to desired MP pose errors.