Abstract
A method for improving the accuracy of a parallel manipulator with full-circle rotation is systematically investigated in this work via kinematic analysis, error modeling, sensitivity analysis, and tolerance allocation. First, a kinematic analysis of the mechanism is made using the space vector chain method. Using the results as a basis, an error model is formulated considering the main error sources. Position and orientation error-mapping models are established by mathematical transformation of the parallelogram structure characteristics. Second, a sensitivity analysis is performed on the geometric error sources. A global sensitivity evaluation index is proposed to evaluate the contribution of the geometric errors to the accuracy of the end-effector. The analysis results provide a theoretical basis for the allocation of tolerances to the parts of the mechanical design. Finally, based on the results of the sensitivity analysis, the design of the tolerances can be solved as a nonlinearly constrained optimization problem. A genetic algorithm is applied to carry out the allocation of the manufacturing tolerances of the parts. Accordingly, the tolerance ranges for nine kinds of geometrical error sources are obtained. The achievements made in this work can also be applied to other similar parallel mechanisms with full-circle rotation to improve error modeling and design accuracy.
Highlights
The industrialization of high-speed parallel robots can be greatly promoted by improving their accuracy
As the foundation of accuracy problems, error modeling can provide a theoretical basis for accurate design and kinematic calibration by establishing the mapping relationship between the pose errors in the end-effector and the geometric error sources of the mechanism
The matrix perturbation method based on Denavit–Hartenberg (D-H) homogeneous transformation is a classical approach for error modeling.[1,2]
Summary
The industrialization of high-speed parallel robots can be greatly promoted by improving their accuracy. As the pose error of lower-mobility parallel manipulators cannot be compensated,[14] these approaches are not suitable for such manipulators Bearing this in mind, Huang et al.,[15] taking a 3-DOF parallel kinematic machine with parallelogram struts as an example, proposed a modeling method to separate the geometric error sources which affect the position and orientation errors in the end-effector. Inverse kinematic analysis[27] is considered to determine the active link position angle ui(i = 1, 2, 3) (the range of u1 and u3 is 0 À p, and the range of u2 is p À 2p) according to the position vector r = ( x y z )T of the reference point A on the moving platform (which is 2l0 and 2b0 in the length and width directions, respectively). B3 1⁄4 À2l1x cos u0 À 2l1y sin u0 C3 1⁄4 x2 þ y2 þ z2 þ l12 À l22 þ l02 þ ðÀ1Þi2l0ðÀx sin u0 þ y cos u0Þ
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