Uncoupled actuation of overconstrained 3T-1R hybrid parallel manipulators

Robotica ◽  
2009 ◽  
Vol 27 (1) ◽  
pp. 103-117 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Lie Group ◽  
Constant Velocity ◽  
Algebraic Approach ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Algebraic Properties ◽  
Lie Subgroup

SUMMARYBased on the Lie-group-algebraic properties of the displacement set and intrinsic coordinate-free geometry, several novel 4-dof overconstrained hybrid parallel manipulators (HPMs) with uncoupled actuation of three spatial translations and one rotation (3T-1R) are proposed. In these HPMs, three limbs are those of Cartesian translational parallel mechanisms (CTPMs) and the fourth limb includes an Oldham-type constant velocity shaft coupling (CVSC). The Lie subgroup of Schoenflies (X) displacements of the displacement Lie group and its mechanical generators with nine categories of their general architectures are recalled. A comprehensive enumeration of all possible Oldham-type CVSC limbs is derived fromX-motion generators. Their constant velocity (CV) transmissions are verified by group-algebraic approach. Then, combining one CTPM and one CVSC, we synthesize a lot of uncoupled 3T-1R overconstrained HPMs, which are classified into nine distinct classes of general architectures. In addition, all possible architectures with at least one hinged parallelogram or with one cylindrical pair are disclosed too. At last, related non-overconstrained HPMs are attained by the addition of one idle pair in each limb of the previous HPMs.

Geometric synthesis of spatial parallel manipulators with fewer than six degrees of freedom

2002 ◽  
Vol 216 (12) ◽  
pp. 1175-1185 ◽  
Author(s):  
T S Zhao ◽  
J S Dai ◽  
Z Huang
Keyword(s):  
Mechanism Design ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Algebraic Approach ◽  
Structural Complexity ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Kinematic Pair ◽  
Type Synthesis ◽  
Six Degrees Of Freedom

Manipulators with fewer than six degrees of freedom meet specific tasks and have the advantage of reducing structural complexity, design redundancy and cost. In order to construct parallel manipulators for given tasks, this paper develops an algebraic approach to type synthesis of spatial parallel mechanisms with fewer than six degrees of freedom based on the screw theory. With the proposed steps (i.e. describing restraining screws, identifying basic kinematic pair (KP) screws reciprocal to the restraining screws, linearly transforming the basic KP screws to obtain equivalent serial limbs and allocating the serial limbs) new parallel mechanisms can be constructed. The approach converts a mechanism design into a screw algebra operation, in which screws describe kinematic pairs and constraints between links. As examples, synthesis procedures of parallel mechanisms with four degrees of freedom are given, from which five novel parallel mechanisms result.

Homokinetic Shaft-Coupling Mechanisms via Double Schoenflies-Motion Generators

2014 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Lie Group ◽  
Constant Velocity ◽  
Geometric Constraints ◽  
Algebraic Properties ◽  
Potential Applications ◽  
Mechanical Generator ◽  
Displacement Group ◽  
Group Compositions ◽  
Coupling Mechanisms ◽  
Group Product

The paper begins with introducing the 5-dimensional (5D) double Schoenflies-motion (X-X motion) set employing the group product of two 4D X-motion subgroups of displacements. Two families of primitive X-X motion generators are briefly outlined. Then, the geometric constraints for homokinetic transmission via Lie-group-algebraic properties of the displacement set are established. After that, using the described mechanical generators of X-X motion as the basic building cell, we geometrically generate two major families of homokinetic shaft-coupling mechanisms characterized by a subchain with a mechanical generator of 5D X-X motion set of displacement. The obtained constant-velocity shaft couplings (CVSC) are isoconstrained linkages with two parallel shaft axes, which will be less sensitive to manufacture errors. In addition, by means of the reordering method for displacement group compositions, more CVSC mechanisms can be further obtained. The simple or special findings stemming from the proposed general architectures are presented for the potential applications too.

Non-overconstrained 3-dof spherical parallel manipulators of type: 3-RCC, 3-CCR, 3-CRC

Robotica ◽  
2005 ◽  
Vol 24 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Mourad Karouia ◽  
Jacques M. Hervé
Keyword(s):  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Structural Type ◽  
Parallel Mechanisms ◽  
Structural Types ◽  
Special Cases ◽  
Algebraic Properties ◽  
Analysis And Synthesis ◽  
Fixed Base ◽  
Type 3

Non-overconstrained 3-dof spherical parallel manipulators of a structural type 3-RCC, 3-CCR, 3-CRC are introduced. The mechanism has three limbs that connect in parallel the moving platform to the fixed base. Each limb is an opened kinematic chain made of a sequence of one revolute pair R and two cylindrical pairs C. The orientation of the end-effector is obtained by actuating simultaneously the three limbs. A structural type analysis and synthesis, which is based on the algebraic properties of a Lie group of the displacement set, is employed to find the geometrical conditions for the assembly of these spherical parallel mechanisms and also the structurally singular configurations. Then an enumeration of the structural types is given and remarkable special cases of orientational mechanisms are also described, namely 3-HGR, 3-RGH and 3-HGH.

Cartesian Parallel Manipulators With Pseudoplanar Limbs

2006 ◽  
Vol 129 (12) ◽  
pp. 1256-1264 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Lie Group ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Linear Dependency ◽  
Algebraic Properties ◽  
Moving Platform ◽  
Three Degree Of Freedom

Based on the Lie-group-algebraic properties of the displacement set, the three-degree-of-freedom (3DOF) pseudoplanar motion often termed Y motion for brevity is first introduced. Then, all possible general architectures of the mechanical generators of a given Y subgroup are obtained by implementing serial arrays of 1DOF Reuleaux pairs or hinged parallelograms. In total, five distinct mechanical generators of Y motion are revealed and seven ones having at least one parallelogram are also derived from them. In order to avoid the singularity that may occur in the limbs, all singular postures of Y-motion generators are also located by detecting the possible linear dependency of the joint twists and the group dependency of displacement sets. The parallel layout of three 4DOF limbs including Y-motion generators with orthogonal planes make up a Cartesian translational parallel manipulator, which produces a motion set of spatial translations. The 3DOF translation of the moving platform is directly controlled by the three 1DOF translations in three orthogonal prismatic fixed joints.

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

scholarly journals Introduction to the special issue: parallel manipulators.

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 353-353
Author(s):  
François Pierrot
Keyword(s):  
North America ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Special Issue ◽  
Industrial Areas

It has been a pleasure for me to arrange this Special Issue of Robotica on Parallel Robots which provides 9 papers from authors from Asia, Oceania, North America and Europe; worldwide research on this topic is proof of the growing interest of both the scientific and the industrial areas of parallel mechanisms. I truly believe that the main reason for this enthusiasm is that parallel mechanisms research extends from theoretical mathematics and kinematics to applied robotics, and even beyond, creating new technological challenges.

A Statically Balanced Gough/Stewart-Type Platform: Conception, Design, and Simulation

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Marco Carricato ◽  
Clément Gosselin
Keyword(s):  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Theoretical Point ◽  
Constant Force ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Neutral Equilibrium ◽  
The Difference ◽  
Elastic Elements

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical designs of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in equilibrium in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. The performance of a study prototype is simulated via a model in both static and dynamic conditions, in order to prove the feasibility of the proposed design. The effects of imperfect balancing, due to the difference between the payload inertial characteristics and the theoretical/nominal ones, are investigated. Under a theoretical point of view, formal and novel derivations are provided of the necessary and sufficient conditions allowing (i) a body arbitrarily rotating in space to rest in neutral equilibrium under the action of general constant-force generators, (ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy, and (iii) a leg of a Gough/Stewart-type manipulator to operate as a constant-force generator.

A Comparison of Architectures of Parallel Mechanisms for Workspace and Kinematic Properties

1995 ◽  
Author(s):  
Clement M. Gosselin ◽  
Rémi Ricard ◽  
Meyer A. Nahon
Keyword(s):  
Parallel Manipulators ◽  
Parallel Architectures ◽  
Parallel Mechanisms ◽  
Design And Optimization ◽  
Stiffness Properties ◽  
Structural Differences ◽  
Six Degree Of Freedom ◽  
Kinematic Properties ◽  
Better Than ◽  
Normalization Factors

Abstract This paper presents a study of the workspace and kinematic properties of four different architectures of six-degree-of-freedom parallel mechanisms. For each architecture, the volume of the Cartesian workspace is computed at different orientations of the moving platform. The distribution of the workspace is also found by computing the 2D sections of the 3D workspace. The rotational workspace is then determined at the reference position of the platform. Finally, the stiffness properties of the architectures are obtained. Normalization factors are then defined to account for the structural differences between the architectures of mechanisms. The comparison of the different architectures of parallel mechanisms has been performed using SIMPA, a specialized CAD tool developed for the kinematic analysis and optimization of parallel manipulators. The results thus obtained illustrate the range of performance which can be expected from different parallel architectures. Although none of the architectures proves to be better than all the others in all respects, particular architectures do excel in particular performance measures. The approach proposed would therefore be useful in further studies relating to the design and optimization of parallel manipulators and mechanisms.

On Anti-Commutative Algebras and Analytic Loops

1965 ◽  
Vol 17 ◽  
pp. 550-558 ◽  
Author(s):  
Arthur A. Sagle
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Binary Operation ◽  
Identity Element ◽  
Unique Element ◽  
Commutative Algebras ◽  
Algebraic Properties

In (4) Malcev generalizes the notion of the Lie algebra of a Lie group to that of an anti-commutative "tangent algebra" of an analytic loop. In this paper we shall discuss these concepts briefly and modify them to the situation where the cancellation laws in the loop are replaced by a unique two-sided inverse. Thus we shall have a set H with a binary operation xy defined on it having the algebraic properties(1.1) H contains a two-sided identity element e;(1.2) for every x ∊ H, there exists a unique element x-1 ∊ H such that xx-1 = x-1x = e;

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