| The traditional 3-DOF(three degrees of freedom) rotational parallel mechanisms are called the spherical parallel mechanisms, whose rotation center is usually the intersecting point of multiple revolute joint axes. This restricted geometric condition is very hard to fulfill in the manufacture and assembly process, which restricts the institution of engineering application in a certain extent. In this paper, we mainly study a class of 3-DOF parallel mechanisms without intersecting axes, which can realize the spatial three-dimensional rotation and has a good application prospect in the field of attitude control.A 3-DOF rotational 3-[RPR]RR parallel mechanism is introduced, and the nature of the degree of freedom of this kind of mechanism is studied by means of Grassmenn line geometry and screw theory. The inverse solution of the mechanism is carried out, and four symmetrical assembly configurations are obtained. Singularity analysis of the mechanism is carried out from three aspects: limb singularity, platform singularity and actuation singularity. A modified Euler angle is adopted to describe the attitude of the mechanism, and the rotational workspace of the mechanism is analyzed.A 3-RPS parallel mechanism which can realize three-dimensional rotation is introduced. When restricted to rotate about the vertical axis, the mechanism can be equivalent to a RPSC spatial single-loop mechanism. Based on the analysis of the single-loop mechanism, a special kind of actuation singularity of the 3-RPS parallel mechanism is determined. It’s also found that the motion of its moving platform is the vertical Darboux motion. Because of the similar motion and constraint characteristics, all of this kind of 3-DOF parallel mechanisms without intersecting axes can realize the vertical Darboux motion, and have similar actuation singularity.Based on the above analysis, a novel 3-PRS 3D rotation platform is presented, and the preliminary design is carried on. The inverse kinematic analysis is conducted and the overall Jacobian matrix of the mechanism is established. The static analysis, stiffness matrix of the mechanism is analyzed. By using a numerical method, the singular locus of the mechanism in its workspace is analyzed.In the end, the structure design and size optimization of the 3-PRS rotational platform prototype is carried out, then the properties of the mechanism are analyzed and verified through the experiments. |
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