Error modeling and singularity analysis of planar parallel mechanisms using optimized expression of joint clearances and link deformation

A fast error modeling method is proposed to analyze the pose deviation of 3-RPR planar parallel mechanisms with multiple revolute joint clearances. The pose error arisen from clearances and limb deformation is modeled from the point of inverse kinematics and estimated numerically. Manipulator poses are represented by elements of the Lie group SE(2) and the discontinuous deformation of limbs due to clearances are modeled by the Heaviside function, which is then approximated with the hyperbolic tangent function. After establishing the error model, an efficient error compensation method is introduced. The proposed error modeling and accuracy analysis method are validated by case study of a 3-RPR mechanism. The results show that the hyperbolic tangent function runs faster than the step function and it provides better convergence. Finally, the singularity of the 3-RPR mechanism with load is analyzed and the results reveal the effects of loads and clearances on mechanism singularities.