New Family of 3-DOF UP-Equivalent Parallel Mechanisms with High Rotational Capability

Abstract

Parallel mechanisms (PMs) having the same motion characteristic with a UP kinematic chain (U denotes a universal joint, and P denotes a prismatic joint) are called UP-equivalent PMs. They can be used in many applications, such as machining and milling. However, the existing UP-equivalent PMs suffer from the disadvantages of strict assembly requirements and limited rotational capability. Type synthesis of UP-equivalent PMs with high rotational capability is presented. The special 2R1T motion is briefly discussed and the fact that the parallel module of the Exechon robot is not a UP-equivalent PM is disclosed. Using the Lie group theory, the kinematic bonds of limb chains and their mechanical generators are presented. Structural conditions for constructing such UP-equivalent PMs are proposed, which results in numerous new architectures of UP-equivalent PMs. The high rotational capability of the synthesized mechanisms is illustrated by an example. The advantages of no strict assembly requirements and high rotational capability of the newly developed PMs will facilitate their applications in the manufacturing industry.

Type Synthesis of Lower Mobility Parallel Mechanisms: A Review

“…For PMs that have motion in the first class, the Lie group theory-based method is still effective. 3R2T PMs [17], 1T2R PMs [18][19][20][21], 3T2R PMs [22], 2R PMs [23], and 2T2R PMs [24,25] have been synthesized. A general formula used in type synthesis is given by where {M} represents the motion set of the moving platform, {L i } the motion set (also called the kinematic bond) allowed by limb i, and n the number of limbs.…”

“…The investigation on systematic type synthesis approaches of lower mobility PMs dates back to the last century and has experienced a gold period with great progress at the beginning of this century. Based on various mathematical tools, a variety of approaches have been presented in the literature, including the Lie group theory-based method [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], the method based on G F (generalized function) sets [30][31][32][33][34][35], linear transformation method [36][37][38][39][40][41][42][43][44][45][46], position and orientation characteristic (POC) set method [47][48][49][50][51][52], finite screw method [53][54][55][56][57][58][59], screw theory-based method …”

Generalized Kinematics Analysis of Hybrid Mechanisms Based on Screw Theory and Lie Groups Lie Algebras

“…Huang et al [19] presented a systematic approach for the kinematic calibration of a 6-DOF hybrid polishing robot and formulated the linearized error model based on screw theory. Li et al [20,21] presented the type synthesis of parallel mechanisms according to screw theory and Lie group. Sun et al [22,23] proposed a generalized method to solve inverse kinematics of serial and parallel mechanisms using finite screw.…”

“…Then, by applying Eqs. (20) and (21), the velocity and acceleration vectors of moving platform of the parallel joints can be obtained. Finally, the kinematics characteristics of all the motion pairs of the hybrid manipulator can be derived by applying Eqs.…”

“…According to Eqs (20). and(21), the velocity and acceleration vectors of moving platforms of the parallel joints can be calculated as:…”