This paper presents a methodology for the Jacobian analysis of limited degrees-of-freedom (DOF) parallel manipulators. A limited-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees-of-freedom. It is shown that a 6 × 6 Jacobian matrix, which provides complete information about singularities, can be derived by making use of the theory of reciprocal screws. The 3-UPU and 3-RPS parallel manipulators are used as examples to demonstrate the methodology.Copyright © 2002 by ASME

Jacobian Analysis of Limited-DOF Parallel Manipulators

The lower-mobility parallel mechanism (PM) has fewer than six degrees of freedom (DoFs) and requires fewer links, joints and actuators than its 6-DoF counterpart. Hence, the use of the lower-mobility PM may save much cost in those applications requiring less mobility. In this paper, the type synthesis of symmetrical lower-mobility PMs is performed systematically using the constraint-synthesis method. First, some important theoretical fundamentals of type synthesis of lower-mobility PMs are investigated, including a classification of symmetry of lower-mobility PMs, the identification of instantaneous mechanisms and input selection method. Moreover, the difficult problem of how to correctly apply the general Grubler-Kutzbach criterion to lower-mobility PMs is solved. A mobility analysis of PMs with a closed loop in the limbs is also presented to demonstrate the validity. The type synthesis of 5-DoF and 4-DoF PMs is then dealt with in detail. Enumerations of novel 5-DoF and 4-DoF PMs are presented. The chara...

Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint-Synthesis Method:

In this paper, a systematic approach is developed for the structural synthesis of a class of four-degrees-of-freedom (4-DoF) and 5-DoF overconstrained parallel manipulators with identical serial limbs. The theory of screws and reciprocal screws is employed for the analysis of the geometric conditions that must be met by the limbs of such parallel manipulators. Limb structures that can be used for constructing 4-DoF or 5-DoF parallel manipulators are enumerated according to the reciprocity of the twist and wrench systems. The assembly conditions of a parallel manipulator built by using identical C- or F-limbs are discussed. Several 4-DoF and 5-DoF parallel manipulators are sketched as examples.

Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators with Identical Limb Structures

The concept of constraint singularity is introduced. This is a phenomenon occurring in parallel mechanisms with reduced freedoms when the screw system, formed by the constraint wrenches in all legs, loses rank.

Constraint singularities of parallel mechanisms

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.Copyright © 2002 by ASME

Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory

A novel three degree-of-freedom manipulator, which includes three in-parallel limbs between a fixed frame and a platform that moves by spherical rotation about a fixed point, is described. This mechanism is not overconstrained and has the structural type of the translational Tsai platform. Each limb is a sequence of a universal joint, a prismatic pair and a universal joint (UPU). The spherical rotation of the moving platform is obtained by variation of length in the linear actuators that are mounted on the prismatic pairs of the three limbs. Under some geometric constraint changes, we obtain a generalised structure of the mechanism. This arrangement belongs to a more general family of mechanisms, which is presented succinctly and can be obtained from deductive reasoning.

M. Karouia

Papers

A Three-dof Tripod for Generating Spherical Rotation