Modelling and calibration of parallel mechanisms using linear optical sensors and a coordinate measuring machine

This paper presents a new procedure for the modelling and calibration of a parallel mechanism by using linear optical sensors and a coordinate measuring machine. Three standard spheres, fixed to the moving platform, were measured by means of a coordinate measuring machine. Additionally, a control algorithm was developed to store sensor readings in each analysed position. These readings and the kinematic model allow us to obtain the calculated sphere coordinates. The use of high-accuracy linear optical sensors allows us to correct actuator backlash, thereby increasing the mechanism accuracy. The developed method defines an objective function that compares the measured and calculated coordinates of the three-sphere centres in order to obtain the identified model parameters that minimize this difference. This procedure combines both inverse and forward kinematics, and solves the nonlinear system loop of the kinematic model inside a second loop that optimizes the geometric parameters of the model. Numerical optimization techniques based on Levenberg–Marquardt algorithm are used to solve both optimization loops. Results show that the platform position and orientation errors are improved by more than one order of magnitude.