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.

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.

Conversaziones and Reception, 1975

1976 ◽  
Vol 30 (2) ◽  
pp. 117-126
Keyword(s):  
Low Power ◽  
Resonance Frequency ◽  
Sliding Friction ◽  
Applied Physics ◽  
Irrigation Systems ◽  
Stirling Cycle ◽  
Potential Applications ◽  
Electrical Generator ◽  
Mechanical Generator ◽  
Coupling Mechanisms

Conversaziones were held this year on 8 May and 26 June. At the first conversazione twenty-five exhibits and two films were shown. Frictionless Stirling-cycle engines were demonstrated by the Electronics and Applied Physics Division, U.K.A.E.A., Harwell. Conventional Stirlingcycle engines running at low power levels are extremely inefficient, owing mainly to the sliding friction associated with the pistons and their coupling mechanisms. Two types of frictionless Stirling-cycle engines have been developed at Harwell. In the thermo-mechanical generator, the output piston of such an engine is replaced by a diaphragm coupled to an electrical generator and the displacer piston is spring mounted, out of contact with the cylinder. The two spring/mass systems are coupled by their common fixing point. This self-starting, frictionless Stirling-cycle engine takes up its own resonance frequency when heat is applied, and has an efficiency of 15% at a 25 W output. An operational prototype generator driving a small television set was shown. Fluidyne is a self-excited, freely oscillating Stirling-cycle engine which needs no solid moving parts and consists simply of two U-tubcs partially filled with liquid; three of the four ends of the U-tubes are connected together through a gas-filled space. The Fluidyne engine has potential applications as a simple pump, e.g. in irrigation systems using solar heat and several versions of the system were shown in operation.

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;

CONJUGATION IN THE DISPLACEMENT GROUP AND MOBILITY IN MECHANISMS

2009 ◽  
Vol 33 (2) ◽  
pp. 163-174 ◽  
Author(s):  
Jacques M. Hervé
Keyword(s):  
Rigid Body ◽  
Lie Group ◽  
Algebraic Structure ◽  
Frame Of Reference ◽  
Mathematical Tool ◽  
Simple Matter ◽  
Rigid Body Motions ◽  
Displacement Group

The paper deals with the Lie group algebraic structure of the set of Euclidean displacements, which represent rigid-body motions. We begin by looking for a representation of a displacement, which is independent of the choice of a frame of reference. Then, it is a simple matter to prove that displacement subgroups may be invariant by conjugation. This mathematical tool is suitable for solving special problems of mobility in mechanisms.

Reconfiguration Techniques and Geometric Constraints of Metamorphic Mechanisms

2009 ◽  
Author(s):  
Liping Zhang ◽  
Jian S. Dai ◽  
Ting-Li Yang
Keyword(s):  
Group Structure ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Geometric Representation ◽  
Group Extensions ◽  
Matrix Operations ◽  
Group Motion ◽  
Displacement Group ◽  
Configuration Changes ◽  
Invariant Configuration

This paper proposes a geometric way to generate metamorphic configurations and investigates metamorphic principles based on geometrized displacement group. Metamorphic reconfiguration techniques are revealed as the variations of kinematic joints, kinematic links and geometric orientation constraints particularly by examining the invariant configuration properties of a mechanism. The nature of all these configuration changes belongs to geometric constraint category. Metamorphic configuration units are proposed as the irreducible reconfiguration modules to envelop these reconfiguration techniques. It can self-reconfigure or be combined to generate metamorphosis. Moreover, the geometrized displacement group is lent to achieve a geometric representation for configuration modelling and further reconfiguration operations. Based on seting up kinematic group extended qualitatively according to its group structure, geometrized displacement group modelling is proposed for these identified metamorphic configuration units. The investigated group motion-matrix is an integration of its displacement group properties and kinematic extensions. Then defined geometric constraint relations and the proposed dependence rules lead to metamorphic principles. In this way, metamorphic process is mapped to matrix operations under group extensions and their compositions. Design examples and a metamorphic joint with six configurations are given to illustrate the feasibility of these metamorphic principles.

Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Guowu Wei ◽  
Yao Chen ◽  
Jian S. Dai
Keyword(s):  
Geometric Constraints ◽  
Reciprocating Motion ◽  
Single Plane ◽  
Plane Symmetric ◽  
Loop Equation ◽  
Dual Plane ◽  
Potential Applications ◽  
Number Synthesis ◽  
First Time ◽  
Geometry And Kinematics

Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grübler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

Three Novel Discontinuously Movable Spatial 7-Link Mechanisms

2006 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Herve´
Keyword(s):  
Lie Group ◽  
Degrees Of Freedom ◽  
Spatial Arrangement ◽  
The Other ◽  
Algebraic Properties ◽  
Relative Motions

Three kinds of new discontinuously movable (DM) spatial 7-link mechanisms named hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6R1P DM mechanisms are synthesized by combining planar and spherical 4R trivial chains. Their discontinuous mobility is explained using the Lie group algebraic properties of the displacement set. In addition, the same given spatial arrangement of joints can be linked in two ways thus constituting two distinct chains with a quite different mobility. One chain has two global degrees of freedom (dofs), which disobey the general Grubler-Kutzbach mobility criterion. The other chain exhibits a singular pose, which is a bifurcation towards two distinct working modes of one-dof mobility. As a result, the set of relative motions between any two specific links is not a manifold but consists of the union of displacement 1-dimensional manifolds.

Case Studies in the Challenge of Properties Design at Nanoscale

2017 ◽  
pp. 148-184
Author(s):  
Marilena Ferbinteanu ◽  
Harry Ramanantoanina ◽  
Fanica Cimpoesu
Keyword(s):  
Case Studies ◽  
Coordination Compounds ◽  
New Technologies ◽  
Molecular Magnetism ◽  
Structure Property ◽  
Potential Applications ◽  
Polynuclear Coordination Compounds ◽  
Coordination Systems ◽  
Coupling Mechanisms ◽  
Structure Calculations

In the quest for nano-sized materials with potential applications in new technologies and devices, the molecular magnetism based on coordination systems shows a valuable path, including the idea of structure-property rationales. Polynuclear coordination compounds are already in the range of nanometers and many consecrated magnetic materials that can be prepared at nano-scale granulation, such as oxides, have as bonding and exchange coupling mechanisms the same causal engines identified in coordination systems. Based on this paradigm, several case studies are taken, relating the magnetic properties with methods of electron structure calculations and phenomenological models.

scholarly journals Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework

2013 ◽  
Vol 469 (2160) ◽  
pp. 20130249 ◽  
Author(s):  
Christopher L. Burnett ◽  
Darryl D. Holm ◽  
David M. Meier
Keyword(s):  
Lie Group ◽  
Trajectory Planning ◽  
Quantum Control ◽  
Higher Order ◽  
Integration Scheme ◽  
Planning Problem ◽  
Lagrange Equations ◽  
Lie Group Action ◽  
Potential Applications ◽  
New Interpretation

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler–Lagrange equations is obtained from a higher-order Hamilton–Pontryagin variational formulation. In this context, the previously known node equations are recovered with a new interpretation as Legendre–Ostrogradsky momenta possessing certain conservation properties. Three example applications are discussed as well as a numerical integration scheme that follows naturally from the Hamilton–Pontryagin principle and preserves the geometric properties of the continuous-time solution.

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