Instantaneous motion analysis of a spherical 3DOF parallel mechanism
                                                                                    SHI Gemeng
                                  （College of Mechanical Engineering, Baoji University of Arts and Sciences, Baoji 721013, China）

Abstract: Aiming at solving the instantaneous location problem of the angle cone on the end member of the spherical 3DOF parallel mechanism with only 3 rotational freedoms，the component finite rotation was expressed by the quaternion algebra, and the mechanisms kinematic analysis was transformed into solving quaternion operator with instantaneous rotation. By analyzing the differential rotation of the angle cone relative to the reference coordinate system on a spherical 3DOF parallel mechanism, a quaternion operator of the motion differential equation describing the instantaneous rotation of the angle cone and the vector equation of the continuous curved surface of the instantaneous rotating axis was established, and the basic solution system of the mechanism motion differential equations was derived. The characteristics of differential motion of a mechanism at a certain moment were quantified by the axode curvature and torsion. With Matlab software, two methods of numerical integration and numerical differentiation were used to obtain the change trajectory of the quaternion operator instantaneous rotation axis and the change curve of the equivalent rotation angle, the change of the axode axis was stable, which indicated that the mechanism had good kinematics character under the kinematic parameters. The prediction value of the truncation error and the accuracy grades of the two numerical methods were given. The simulation results indicate that the accuracy of the numerical integration method is slightly higher.

Key words: spherical parallel mechanism; quaternion algebra; motion differential equations; numerical integration