KINEMATICS OF A FAMILY OF 3T1R PARALLEL MANIPULATORS WITH SIMPLIFIED STRUCTURES

This paper presents a kinematic analysis of a family of 3T1R parallel mechanisms with prismatic actuators. This family is bifurcated into two categories: one featuring a 4-RPUR structure and another with 4-PRUR structure. The paper presents techniques for the construction of parallel manipulators with simplified kinematic structures. Firstly, the 4-RPUR category is investigated. The fundamental 4-RPUR design is presented and subsequently two simplified variants, namely, design 4-RPUR-A and design 4-RPUR-B, are introduced. Similarly, three 4-PRUR parallel manipulators are proposed encompassing a fundamental design and two simplified alternatives. RPUR limb singularities are determined using screw theory and then analyzed in exquisite detail and illustrated. Furthermore, the implications of lost motions within the limb singular configurations are characterized. A constraint -singularity analysis of the three 4RPUR parallel manipulators is conducted as well. Results reveal that these manipulators are constraint -singularity free. Furthermore, the actuation singularities are listed and illustrated for the simplified design B of the 4-RPUR parallel mechanism along with interpretation and an analysis of the uncontrolled motions related to these singularities. The 4RPUR designs exhibit a multitude of noteworthy kinematic features. Notably, in addition to the inherent absence of constraint singularities within the three studied 4RPUR manipulators, a detailed analysis of limb and actuation singularities within the streamlined "design B" has revealed that many of these conditions are either intrinsically implausible or can be avoided through design considerations. This underscores the promising potential and practical viability of the 4RPUR designs, especially "design B".