Study On Symmetrical 2R1T Parallel Mechanism Without Parasitic Motion

The symmetrical parallel mechanisms with two rotational and one translational(2R1T) degrees of freedom(DOFs) have wide application prospects in the manufacturing industry. However, all the existing 2R1 T symmetrical parallel mechanisms(PMs) have the problem of parasitic motion which brings much difficulty in the calibration and path planning, and severely restricts the applications of this kind of parallel mechanisms. In order to solve the problem, a novel class of symmetrical 2R1 T parallel mechanisms without parasitic motion are proposed in this paper, including the novel 3-UPU PM, the SNU 3-UPU PM and another new 3-UPU PM. Moreover, analysis about these PMs has been done.A novel 3-UPU PM without parasitic motion is proposed. Its mobility property is studied by using the the screw theory. It turns out that the moving platform can rotate continually about any axis or point on the mid-plane; Inverse kinematics and forward kinematics of this mechanism are studied. The workspace of this mechanism is drawn out. By using the theory of kinematic influence coefficient, the relationship between the velocity and acceleration of the moving platform and the driver are obtained. Its singularities are talked about including limb singularity, platform singularity and actuation singularity.It is discovered when the mobility of SNU 3-UPU PM is 2R1 T, it has no parasitic motion, besides that, the SNU 3-UPU PM has very similar motion characteristics as the novel 3-UPU PM. By using the screw theory and geometric principle, its movility properties and motion characteristics are studied carefully. The expression of inverse kinematics of this mechanism is obtained. Moreover, the trajectory planning and numerical example of continuous translation and rotation are presented.The fundamental features of this class of PMs without parasitic motion are discovered, and the principle of pure equivalent rotation is introduced. A new 3-UPU PM is gotten by combining the features of the novel 3-UPU PM and the SNU 3-UPU PM. The base and platform of this mechanism doesn’t need to be equal, however, it also has no parasitic motion. Besides, it can rotate continually about any axis on the moving platform plane. Its inverse kinematics are analyzed, and numerical examples of continuous rotation about fixed axis are presented. The principle of pure equivalent rotation is find out, which can apply to all these class of 2R1 T PMs without parasitic motion. The correctness of this principle is proved, and the trajectory planning method and numerical example are presented.