Realizing Orthogonal Motions With Wire Flexures Connected in Parallel

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Hai-Jun Su ◽  
Hafez Tari
Keyword(s):  
Screw Theory ◽  
Degree Of Freedom ◽  
Design Approach ◽  
Theory Approach ◽  
Mobility Pattern ◽  
Type Synthesis ◽  
Simply Connected ◽  
Typical Design

In this paper, we study the type synthesis of wire flexures to achieve orthogonal motions by using a recently developed screw theory based design approach. For a given desired mobility pattern, our goal is to find a system of wire flexures that are simply connected in parallel between the functional stage and the ground. It has been shown that a wire flexure is essentially a pure force or a line screw. An n degree-of-freedom (DOF) motion space (allowable motion) is realizable if its reciprocal constraint space can be spanned by 6-n line screws or forces. We first enumerate 34 possible 1–5DOF spaces that are formed by motions along the coordinate axes attached on the functional stage. For each of these 34 motion spaces, we apply the screw theory approach to find its reciprocal force space as well as its rank. At last, a typical design is provided for each of these motion spaces.

Realizing Orthogonal Motions With Wire Flexures Connected in Parallel

2010 ◽  
Author(s):  
Hai-Jun Su ◽  
Hafez Tari
Keyword(s):  
Screw Theory ◽  
Theory Approach ◽  
Mobility Pattern ◽  
Simply Connected

In this paper, we study the synthesis of wire flexures to achieve orthogonal motion by using a recently developed screw theory based approach. For a given desired mobility pattern, our goal is to find a system of wire flexures that are simply connected in parallel between the functional stage and the ground. It has been shown that a wire flexure is essentially a pure force or a line screw. An n dof motion space (allowable motion) is realizable if its reciprocal constraint space can be spanned by 6 – n line screws or forces. We first enumerate all possible one to five degree of motion spaces that are formed by motions along the coordinate axes attached on the functional stage. For each of these 34 motion spaces, we apply the screw theory approach to find its reciprocal force space as well as its rank. We conclude that 18 of them are realizable, 4 are realizable only when their pitches have opposite signs and 12 are not realizable. For each of these 34 cases, we provide an example showing the maximum number of independent wire flexures.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

scholarly journals A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

2009 ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Type Synthesis ◽  
Precision Engineering ◽  
Pattern Design ◽  
Design Constraint ◽  
Systematic Formulation

This paper presents a screw theory based approach for the type synthesis of compliant mechanisms with flexures. We provide a systematic formulation of the constraint-based approach which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint which can be described a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis and constraint pattern design are discussed with examples in details. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

scholarly journals Type Synthesis of Two DOF Hybrid Translational Parallel Manipulators

2016 ◽  
Vol 836 ◽  
pp. 48-53 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Screw Theory ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Type Synthesis ◽  
In Series ◽  
Actuation Scheme ◽  
Two Degree Of Freedom

This paper introduces a methodology for the type synthesis of two degree-of-freedom hybrid translational manipulators with identical legs. The type synthesis method is based upon the screw theory. Three types of two degree-of-freedom hybrid translational manipulators with identical legs are identified based upon their wrench decomposition. Each leg of the manipulators is composed of a proximal module and a distal module mounted in series. The assembly conditions and the validity of the actuation scheme are also defined. Eventually, some novel two degree-of-freedom hybrid translational manipulators are synthesized with the proposed procedure.

scholarly journals Type Synthesis Principle and Practice of Flexure Systems in the Framework of Screw Theory: Part III—Numerations and Synthesis of Flexure Mechanisms

2010 ◽  
Author(s):  
S. Z. Li ◽  
J. J. Yu ◽  
X. Pei ◽  
Hai-jun Su ◽  
J. B. Hopkins ◽  
...  
Keyword(s):  
High Precision ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Type Synthesis ◽  
General Design ◽  
Flexure Mechanism ◽  
Design Philosophy ◽  
Large Motion ◽  
Application Requirements ◽  
Made In

In recent years, the increasing of application requirements call for development of a variety of flexure mechanisms with high precision or large motion and both. Therefore, in Part III of this series of papers we demonstrate how to use the methodology addressed in Part I to synthesize concepts for two kinds of flexure mechanisms, i.e. kinematics-type flexure mechanisms (KFMs) and constraint-type flexure mechanisms (CFMs) with the specified-DOF (Degree of Freedom) characteristics. Although most of them utilize parallel configurations and flexure elements, there is a clear difference in the behavior of flexures between KFMs and CFMs, The resultant type synthesis approaches fall into two distinct categories i.e. freedom-based and constraint-based one, both of which have presented in Part I. In order to derive useful flexure mechanism concepts available for different applications, a general design philosophy and rules are summarized firstly. As the main content of this part, the classifications, numerations, and synthesis for KFMs and CFMs are made in a systematic way. As a result, a majority of new precision flexure mechanisms are developed. In addition, qualitative comparisons are provided to demonstrate the performance and application differences between kinematic-type and constraint-type flexure mechanisms with the same DOF.

Type Synthesis of Three-Degree-of-Freedom Translational Compliant Parallel Mechanisms

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Cong Yue ◽  
Ying Zhang ◽  
Hai-Jun Su ◽  
Xianwen Kong
Keyword(s):  
Screw Theory ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Design Stage ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Geometric Conditions ◽  
Synthesis Procedure ◽  
Flexure Joints ◽  
Three Degree Of Freedom

In this paper, we apply screw theory to type synthesis of compliant parallel mechanisms (PMs) with translational degree-of-freedom (DOF). Compliant PMs are formed by a moving platform supported by three or more limbs each of which is a serial chain of flexure joints and rigid bodies. They achieve movement through the deformation of flexure joints and have been widely used in precision machinery. As an important task in the conceptual design stage, the goal of type synthesis is to determine the chain of each limb as well as their relationship when they are assembled in parallel for a prescribed motion pattern. In our approach, we study a category of commonly used flexure primitives and flexure elements whose freedom and constraint spaces are characterized by twists and wrenches in screw theory. Following the well-studied synthesis procedure for rigid body PMs, we propose a synthesis procedure for compliant PMs via screw theory. As an example, we demonstrate the procedure for synthesizing compliant PMs with three translational DOF. Tables of limbs, types, and geometric conditions for the assemblies of these limbs are presented. The paper provides a catalog of 3DOF translational compliant PM designs. At last, we developed finite element simulation to validate one of the synthesized designs.

Type Synthesis of 3-DOF Rotational Parallel Mechanisms With No Intersecting Axes

2012 ◽  
Author(s):  
Ziming Chen ◽  
Wen-ao Cao ◽  
Zhen Huang
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Constraint Force ◽  
New Approach ◽  
Spherical Parallel Mechanism ◽  
Rotational Motions

Parallel mechanisms which can realize three rotational motions are very important in the parallel mechanism family. Not the same with the traditional spherical parallel mechanism, a new kind of 3-DOF (degree of freedom) rotational parallel mechanism with no intersecting axes (RPMNIA) are proposed in this paper. This kind of rotational parallel mechanisms have the advantages of easy manufacturing. A new approach using the screw theory and the subchain theory is proposed to design the branches with only one constraint force and some new one-force-branches are found. Using these new branches, a group of 3-DOF rotational parallel mechanisms without intersecting axes are synthesized.

CONTROL OF THE DIFFERENTIALLY FLAT LORENZ SYSTEM

2001 ◽  
Vol 11 (07) ◽  
pp. 1989-1996 ◽  
Author(s):  
JIN MAN JOO ◽  
JIN BAE PARK
Keyword(s):  
Equilibrium State ◽  
Lorenz System ◽  
Degree Of Freedom ◽  
Design Approach ◽  
State Trajectory ◽  
System A ◽  
Full State ◽  
Tracking Controller ◽  
The Lorenz System ◽  
Two Degree Of Freedom

This paper presents an approach for the control of the Lorenz system. We first show that the controlled Lorenz system is differentially flat and then compute the flat output of the Lorenz system. A two degree of freedom design approach is proposed such that the generation of full state feasible trajectory incorporates with the design of a tracking controller via the flat output. The stabilization of an equilibrium state and the tracking of a feasible state trajectory are illustrated.

Analysis of Five-Degree-of-Freedom Robot Arms

1983 ◽  
Vol 105 (1) ◽  
pp. 23-27 ◽  
Author(s):  
K. Sugimoto ◽  
J. Duffy
Keyword(s):  
Arc Welding ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Industrial Robot ◽  
Degree Of Freedom ◽  
Numerical Example ◽  
Robot Arms ◽  
Special Cases ◽  
Computer Controlled ◽  
Five Axes

Many kinds of robot arms with five degrees of freedom are widely used in industry for arc welding, spray painting, assembling etc. It is necessary to be able to compute joint displacements when such devices are computer controlled. A solution to this problem is presented and the analysis is illustrated by a numerical example using the most common industrial robot with five axes. Further, special cases are discussed using screw theory.

Analysis of Parasitic Motion in Compliant Mechanisms Using Eigenwrenches and Eigentwists

2018 ◽  
Author(s):  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Degree Of Freedom ◽  
Compliance Matrix ◽  
Parasitic Motion ◽  
Actual Degree ◽  
Motion Metrics ◽  
Mechanism Kinematic ◽  
Kinematic Information

Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.

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