A Micro-Deformation Model of Parallel Manipulators in the Gravity Field

Establishing a microelastic deformation (micro-deformation) model of parallel manipulators (PMs) in the gravity field is of great significance for improving the calibration accuracy. Gravity affects the limb constraint wrenches space of PMs, resulting in the end-point micro-deformation, which damages end-point accuracy. A modeling method was proposed for the micro-deformation analysis of PMs with the consideration of gravity and the flexibility of rods and actuators based on the screw theory to fix this issue. First, the mechanism was considered an open-loop structure by cutting joints at the connection between limbs and moving platform. The limb constraint wrenches system and limb stiffness matrix were determined based on the screw theory and strain energy methods. Then, the limb gravity-additional constraint wrenches induced by gravity were established based on the reciprocity product of the twist screw and the constraint wrenches being zero. Meanwhile, the projection of limb deformations caused by gravity in the direction of the constraint wrenches system was established. Finally, an analytical methodology of the end-point micro-deformation of PMs with the consideration of gravity was built by means of the virtual work principle. The work decoupled the influences of gravity and the external load on the micro-deformation of the mechanism. The comparison between the results of the analytical model and finite element model of the line body and solid body of the 3PRRR over-constrained PM showed that the maximum error of the linear micro-deformation was within 3% and 11%, respectively.