In this paper, the design of a spherical three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Three different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) workspace maximization, and (c) isotropy. The associated problems are formulated and their solutions, one of them requiring to resort to a numerical method, are provided. Optimum designs are thereby obtained. A discussion on singularities is also included.
A spherical parallel manipulator (SPM) refers to a 3-DOF parallel manipulator in which the moving platform has only three pure rotational degrees of freedom of motion relative to the base. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the input validity check of SPMs are dealt with in sequence. SPKCs with and without inactive joints are synthesized. The number of over-constraints of each SPKC is also given. The phenomenon of dependent joint groups in a SPKC is revealed for the first time. The input validity check of SPMs is also simplified.
This paper introduces several new types of parallel mechanisms with prismatic actuators whose degree of freedom is dependent on a constraining passive leg connecting the base and the platform. A general kinetostatic model is established for the analysis of the structural rigidity and accuracy of this family of mechanisms. The geometric model of this class of mechanisms is first introduced. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, a few examples are given to illustrate the results.
This paper studies the kinematic geometry of a special 6-RUS parallel manipulator for which the axes of all base actuated R-joints coincide, the centers of all U-joints move along the same circular track, and the platform S-joints coincide in pairs. Particularly, the paper presents a geometric algorithm for the computation of the constant-orientation workspace. An already known methodology has been enhanced to include the physical constraint, modelled as three Bohemian dome surfaces, on the U-joint interference. In addition, the singularity loci for a constant orientation are shown to form a quartic surface. The workspace boundaries and the singularity loci are analytically computed and represented as horizontal cross-sections. Important observations are made on the singularities of general parallel mechanisms with pair-wise coincident S-joints. The paper also introduces the phenomenon that the workspace of some parallel mechanisms is divided into regions corresponding to different branch sets.
This paper presents a detailed analysis of the constant-orientation wrench-closure workspace of planar three-degree-of-freedom parallel mechanisms driven by four cables. The constant-orientation wrench-closure workspace is defined as the subset of the plane wherein, for a given orientation of the moving platform, any planar wrench applied on the moving platform can be balanced by the cable-driven mechanism. Based on mathematical observations, this workspace is proved to be the union of two disconnected sets that may or may not exist. Moreover, if the constant-orientation wrench-closure workspace (WCW) exists, its boundary is shown to be composed of portions of conic sections. Then, an algorithm that determines the constant-orientation wrench-closure workspace by means of a graphical representation of its boundary is introduced. Several examples are also included.
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