Compliance error modeling for manipulators considering the effects of the component weights and the body and joint flexibilities

Next, a parallel robot with 3-RUU kinematic chain is considered as a case study. Using the concept of Wrench Jacobian Matrices (WJMs), the internal wrench of each flexible component is calculated. The internal wrenches are obtained, for all the robot's configurations over its entire workspace, as functions of the external wrenches applied to the end-effector and distributed weights of the robot's moving bodies. The WJMs are used to calculate the compliance matrices of flexible components as well as overall compliance matrix of the robot. Using the overall compliance matrix of the robot and applying a computational algorithm, a comprehensive study is performed to evaluate the effects of the components' flexibility on accuracy of the robot. Finally, the range of the total compliance error is calculated throughout the robot's workspace. The total error range is calculated according to the physical characteristics of the robot and allowable range of the external wrenches applied to the end-effector. For this purpose, a general compliance error range (GCER) is defined throughout the robot's workspace. The GCER defines accuracy interval of the robot's end-effector with respect to the flexibility-induced errors of compliant modules.