Error Compensation System for Joints, Links and Machine Frame of Parallel Kinematics Machines

This paper describes error compensation methods for parallel kinematics machines (PKMs). First, joint errors and link deformations caused by external forces and heat are discussed. Because a linear scale unit is connected to each spherical joint located at both ends of an extensible limb through two rods, the scale unit can measure not only displacement of the prismatic joint but also the limb’s deformation. Moreover, the scale unit also measures the joint’s runout and its deformation in the limb’s direction because the rod end is in contact with the sphere of the spherical joint. Consequently, the unit accurately measures any change in the distance between the spherical joints independent of the external force. Further, temperature fluctuation has little effect on measured distance because the rods are made of a low expansion alloy. This device was built using experimental limbs and tested for use with coordinate measuring machines. Results showed that, without any additional sensor, the device acquired the same effect; it improved the stiffness and the thermal coefficient of expansion of the whole limb. Secondly, another compensation method for elastic and thermal deformations of the machine frame supporting the mechanism is proposed. Nine displacement sensors with Super-Invar rods measure the distance between the surface place and three joint supports or the base platform of the PKM. Then, the forward kinematics of the hexapod mechanism calculates displacement and orientation variations of the base platform during operation from these measured displacements. Consequently, coordinates of the PKM’s end-effector can be compensated by the dimensions, the displacement, and the orientation of the base platform during operation. This device was installed in the experimental coordinate measuring machine. Coordinate measurements using a master ball mounted on the surface plate showed that this device decreased the influences of temperature fluctuation and external force on machine accuracy. The International Journal of Robotics Research Vol. 24, No. 12, December 2005, pp. 1087-1102, DOI: 10.1177/0278364905060149 ©2005 Sage Publications KEY WORDS—parallel kinematics machine, error compensation, joint runout, joint deformation, frame deformation, thermal expansion, machine tool, coordinate measuring machine