Accurate assessment of the robots’ stiffness is a difficult step in calculating the effect of the components flexibility on the accuracy and performance of the robots. This difficulty is sometimes resulted from the complex geometries of the flexible components of the robots. This paper proposes an exact analytical method for calculation of the robots’ stiffness which can be readily extended to all the robot types with complex geometries. The proposed method is based on the Castigliano’s second theorem and calculation of the strain energies of the flexible components. This method significantly reduces the need for the simplifications commonly made in the modeling of the stiffness matrix of the robots. Unlike the traditional methods, the proposed method can consider the effects of the distributed loads applied to the robot and the distributed weights of the components. Moreover, the bending moments, shear forces and torsional moments applied to each component of the robot can be considered. The robot’s structure is modeled as a distributed system and the position error of the end–effector is calculated as a function of the flexibility of all bodies and joints. 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.

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