Qiang Zeng

This paper presents a novel 4-DOF kinematotropic hybrid parallel manipulator. The topological structure allows for the realization of two translatory and two rotary output motions. Both the translations and rotations take place only in two orthogonal axes. The rotations are designed to possess the kinematotropic property, namely the output mobility of the manipulator can be changed while the topological structure remains invariable. In the process of the topological synthesis, two types of topological arrangements of the kinematotropic hybrid parallel manipulators are developed in the form of multiply moving platforms and subchains based on displacement group theory and mathematical logic. Kinematic modeling of the most feasible kinematotropic hybrid parallel manipulator is performed by obtaining its kinematic forward and inverse solutions and velocities. Suitable drive methods are also defined. At last, a prototype of the analyzed kinematotropic hybrid parallel manipulator is built to evaluate the feasibility of the developed design method, validate the kinematic modeling, and establish the manipulator’s kinematotropic properties.

This paper analyzes the basic forms of 4-DOF spatial motions through the introduction of logical propositions for the topological structural synthesis of multiloop hybrid spatial mechanisms. The proposed method for the topological structural synthesis is based on displacement group theory and consists of two elements. First, spatial multiloop detachment (SMD) is proposed for the analysis of the output motion relations in multiloop topological arrangements. Second, configuration cards for displacement subsets of subchains (CCDS) are developed for subchain design. To demonstrate the applicability of SMD and CCDS to the four basic forms of 4-DOF motions, 12 novel serial-parallel hybrid mechanisms are synthesized that include the nonspanning tree netted form of topological arrangements.

SUMMARY: This paper introduces the mathematical logical proposition into kinematics and presents a novel method for topological design and representation of mechanisms. The six-value non-classical logical matrix in three orders is proposed to represent spatial basic motions, relations, and selection of moving reference frame. The combinatorial logical sets of mechanisms are built and axiomatized to analyze serial–parallel hybrid mechanisms. In accordance to the logical relations, the mapping between topological arrangement and topological geometry is developed, and algorithm of decomposition synthesis is presented. Furthermore, the higher dimensional topological arrangement of multi-loop hybrid mechanism can be obtained by mapping of higher dimensional geometry. At last, four typical examples are developed to illustrate application of method of logical proposition in topological design of mechanisms. The method is helpful for topological design and analysis of multi-loop hybrid mechanisms.

This paper presents a systematic approach on structural synthesis of serial-parallel hybrid mechanisms from the point of displacement group theory and mathematical logic. The hybrid mechanisms can be represented by binary 12 bit string matrix, where the lower 4 bits represents the universal set of spatial displacement subsets, while the higher 8 bits represents the two-order adjacent relations of spatial displacement subsets. Meanwhile, the concept of an arrangement matrix and three types of fractal operations can be developed. Utilizing the novel representational approach of mechanisms, the displacement subsets and spatial adjacent relations can be operated in logical matrices based on the given mapping of logical matrix operation. The binary logical mirror coordinate system of mechanisms is developed by logical representations. Finally, an example of structural synthesis of hybrid mechanism (two-order hybrid mechanism) is introduced using the proposed approach. The approach is helpful for the processing of serial-parallel hybrid mechanism designs.