Error Compensation System for Joints, Links and Mechine Frame of Parallel Kinematic Machine

This study deals with compensation methods for deformations of both the links of the parallel kinematic mechanism and the flame supporting the mechanism. These deformations are caused by the heat, the external forces and the internal forces. First, the longitudinal deformation of the prismatic joints is mechanically compensated by Super-Invar rod connected to the joints and the linear scale units. Second, nine displacement sensors with nine Super-Invar rods measure the variation of distances between the surface plate and three spherical joint supports. The direct kinematics of Hexapod mechanism calculates the displacement and the attitude variations of the mechanism during operation. Consequently, the coordinates of the end effector are compensated. Experimental results show reduction of the influence of the temperature fluctuation and variation of measured values.

Key words: parallel kinematic machine, error compensation, motion error, thermal expansion

Fig. Improved extensible strut. Scale unit accurately measures change in distance between spherical joints regardless of deformations of joints and links.

Fig. Measurement device for frame deformation using Super-Invar rods and displacement sensors


Fig. Displacement measurement sensors for runouts and elastic deformations of the revolutionary joints of the PKM. These compensation systems are installed in a coordinate measuring machine built in our laboratory.

Fig. Super-Invar rods to compensate for link thermal deformations.

Fig. Nine sets of displacement sensors and Super-Invar rods measure change in the size and motion error of the base platform of PKM.


Published paper

  1. Takaaki OIWA and Yuuya TERASAWA: Compensation System for Machine Frame Deformations of Parallel Kinematic Machine (Abbe's principle-based Improvement of compensation device), Transactions of the Japan Society of Mechanical Engineers, Vol. C79, No. 808 (2013) 5103-5116 (in Japanese).
  2. Takaaki OIWA: Error Compensation System for Joints, Links and Mechine Frame of Parallel Kinematics Machines, International Journal of Robotics Research, Vol. 24, No. 12 (2005), pp. 1087-1102.


  1. Takaaki OIWA: Accuracy Improvement of Parallel Kinematic Machine-Error Compensation Methods for Elastic and Thermal Deformations of Joints, Links and Machine Frame, The 6th International Workshop of the Department of Mechanical Sciences and Engineering , 33-38 2003.
  2. Takaaki OIWA: Accuracy Improvement of Parallel Kinematic Machine, The euspen International Topical conference 2003 on Precision Engineering, Micro-Technology, Measurement Techniques and Equipment, Vol.1, pp.125-128. 2003
  3. Takaaki OIWA: Study on Accuracy Improvement of Parallel Kinematic Machine (Compensation Methods for Thermal Expansion of Link and Machine Frame), The 1st Korea-Japan Conference on Positioning Technology (CPT2002),
  4. Takaaki OIWA: Accuracy Improvement of Parallel Kinematic Machine -Error Compensation System for Joints, Links and Machine Frame-, 6th International Conference on Mechatronics Technology (ICMT2002), September 29 - October 3, 2002, Kitakyushu, JAPAN,pp433-438.

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