The Stewart platform manipulator: a review

The Kutzbach-Grubler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Mobility of Overconstrained Parallel Mechanisms

In the area of parallel robots, the use of lower-mobility parallel manipulators for many tasks requiring fewer than six degrees of freedom (DoF) has drawn a lot of interest. This paper treats one fundamental problem in the study of lower-mobility parallel manipulators: type synthesis. Using reciprocal screw theory, we define the mechanism constraint system and limb constraint system. We then investigate the relations between the mechanism constraint system and the limb constraint system under different geometrical conditions. Three tables describing the relations are presented. Based on the three tables, we propose a constraint-synthesis method for type synthesis of symmetrical lower-mobility parallel manipulators. The method used in the paper to construct the kinematic structure of the limb of lower-mobility parallel manipulators with prescribed DoF is simple and systematic. Examples are included to illustrate the application of the method and some novel lower-mobility parallel manipulators with 3-, 4- a...

General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel 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:

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

The use of lower mobility parallel manipulators with less than six degrees of freedom (DOFs) has drawn a lot of interest in the area of parallel robots In this paper, the type synthesis of 3R2T 5-DOF parallel mechanisms (PMs) is performed systematically using the Lie group of displacements, where R denotes a rotational DOF, and T denotes a translational DOF First, some necessary theoretical fundamentals about the displacement group are recalled Then, a general approach is proposed for the type synthesis of 3R2T 5-DOF PMs The limb kinematic chains, which produce the desired displacement manifolds, are synthesized and enumerated Structural conditions, which guarantee that the intersection of the displacement manifolds generated by the limb is the desired 5-DOF manifold, are presented An exhaustive enumeration of 3R2T 5-DOF symmetrical PMs is obtained Finally, an input selection method is proposed

Zhen Huang

Papers

General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators

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

Type synthesis of 3R2T 5-DOF parallel mechanisms using the Lie group of displacements

Kinematic characteristics analysis of 3 DOF in-parallel actuated pyramid mechanism☆

Isomorphism identification of graphs : Especially for the graphs of kinematic chains