A calibration method for overconstrained spatial translational parallel manipulators. (June 2019) - Li, Fengchun; Zeng, Qiang; Ehmann, Kornel F; Cao, Jian; Li, Tiemin
Highlights: Replaced the redundant constraints of the overconstrained mechanism with forces. Transformed the overconstrained mechanism to a non-overconstained mechanism. Established a mechanical model to derive the deformation caused by inner forces. The inner force-induced deformation was added into the total kinematic model. The accuracy of the robot can be improved from 1.635 mm to 0.155 mm. Abstract: A calibration method for overconstrained spatial translational parallel mechanisms is proposed. The calibration of a Tri-pyramid overconstrained parallel robot is used as a vehicle to demonstrate the methodology and verify its feasibility. The proposed methodology consists of transforming the overconstrained mechanism of the robot into a non-overconstrained mechanism by replacing its redundant constraints with generalized forces (couples). The kinematic model of the non-overconstrained mechanism is derived using vector loops while its mechanical model is established by the energy method. An integrated kinematic model of the original overconstrained parallel robot is subsequently established by expressing the actual position of the end effector as the sum of the position derived by the kinematic model of the non-overconstrained mechanism and of the force-induced deformations at the end effector derived from the mechanical model. To assess the feasibility and the attainable improvements in accuracy through calibration, the positions of the end effector of the Tri-pyramid robot were measured by a method that uses a Double Ball Bar (DBB) and a 3-axes linear stage with micrometers. Based on the integrated kinematic model of the robot and the measured data, its structural parameters were identified by the Newton–Raphson iteration and least squares methods to complete the calibration. The calibration result shows that accuracy improvements on the order of 90% are achievable.