Theoretical Analysis And Simulation On The Movement Performance Of 3-Dof Parallel Pyramid Mechanism

The modern mechanics plays a dominating role in analyzing new machines applicable for the modernization production, which is useful for clear orientation of the applications and innovations. The new machines are often made of mechanisms with inherent and specific features, which is favorable to develop resources so as to better serve the social life. In the paper, the kinematic performance of 3-DOF parallel pyramid mechanisms, especially the 3-RPS and 3-(RP)S pyramid mechanisms are analyzed and simulated under the support of National Nature Science Foundation. The main contents of this paper are as follows:In this paper, the mobility of the 3-RPS pyramid mechanism is firstly analyzed. This mechanism has three rotations, the axes of which are fixed under the initial displacement while that is always mutative under any other configuration. The paper also judges the rationality of input selection. Then it builds the equations for inverse problem and obtains the three input parameters according to the structure constraints and homogeneous transforming matrixes. Similar to other parallel mechanisms, it is also difficult to get the direct problem of the 3-RPS pyramid mechanism. The orientation is successfully determined by coordinate transformations in terms of the special geometric conditions. Furthermore, the numerical values of direct and inverse problems under certain condition are calculated.The paper extends the plane CARDAN motion which is similar to the inside mesh movement of two gears. The kinematic loci of the representative points are analyzed in detail. It is proved that the 3-RPS pyramid mechanism also has the three-dimensional CARDAN motion and the kinematic trajectory is an ellipse cluster.The motions of the 3-RPS pyramid mechanism are simulated using MATLAB, which indicates that this mechanism is the special one among diverse mechanisms. The 3-RPS pyramid mechanism has three-dimensional CARDAN and helical motions and its workspace is larger than that of the platform manipulator. Since the axes of three rotations are not intersecting, it is comparatively easy to be manufactured than that of the spherical parallel mechanisms. In addition, the mechanism can be applied to lange-angle rotations because of the various axes of motions.The instantaneous motions of the 3-(RP)S pyramid mechanism are analyzed and the principal screws under three different configurations are identified by means of the conic section and the quadric degenerating theory, respectively. The relations between the pitches of the output twists and hree velocity inputs are described, and the spatial distribution of the axes of all the twists with the same pitch is illustrated under each configuration. It is concluded that the motions of this mechanism belong to the first special three-system under the first two configurations, while it belongs to a general third-order screw system under a general configuration. The axes of all the screws with the same pitch lie in a hyperboloid. The above study helps us comprehend the instantaneous kinematic property of the 3-(RP)S pyramid mechanism on the whole, and lays a foundation of the research on the kinematic laws and applications of other pyramid mechanisms.