A Class of Symmetrical 3T, 3T-1R, and 3R Mechanisms With Parallel Linear Motion Elements

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Yi Yang ◽  
Wuxiang Zhang ◽  
Huayan Pu ◽  
Yan Peng
Keyword(s):  
Rotational Motion ◽  
Screw Theory ◽  
Translational Motion ◽  
Kinematic Chain ◽  
Linear Motion ◽  
Kinematic Chains ◽  
Lower Mobility ◽  
Kinematic Performance ◽  
Linear Actuators ◽  
First Time

A kind of kinematic chain with parallel linear motion elements (PLMEs) is proposed and studied in this paper. Based on screw theory, the kinematic screw equations of these linkages are established. The two special categories of PLMEs, with pure translational motion and with pure rotational motion respectively, are identified. The mobilities and the singularities of these kinematic chains are also investigated. By the utilization of these PLMEs, three types of the compound limbs are invented and analyzed. Through assembling these compound limbs in different ways, a class of lower mobility symmetrical 3T, 3T-1R, and 3R mechanisms is synthesized and presented for the first time. The simplified kinematic equations for this class of mechanisms driven by the linear actuators are derived. And the workspaces, singularities, and kinematic performance are addressed. Finally, three typical prototypes with regard to 3T, 3T-1R, and 3R mechanisms are manufactured and experimented to validate the mobility and motion feasibility of these mechanisms.

Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory1

2004 ◽  
Vol 126 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
General Procedure ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Validity Condition ◽  
First Time ◽  
Spherical Parallel Manipulator ◽  
Selection Of

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. 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 selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time.

A Survey of One Class of 7-Jointed Serially Connected Robots: Type-Synthesis to Obtain Controllably Dexterous Workspace

1989 ◽  
Vol 111 (2) ◽  
pp. 163-175 ◽  
Author(s):  
J. K. Davidson
Keyword(s):  
Screw Theory ◽  
Kinematic Chain ◽  
Synthesis Process ◽  
Geometric Description ◽  
Type Synthesis ◽  
End Effector ◽  
Identification Process ◽  
Kinematic Chains ◽  
Five Axes

A type-synthesis process, which is based on screw theory and geometry, is developed to identify certain robots, each of which can provide controllably dexterous workspace of a tool-point. The identification process is confined to only those robots which control the motion of the end-effector with seven series-connected joints, the axes for the outermost three of which are concurrent. Forty six types of robots are so identified, and, for each, the results are (i) a suitable kinematic chain for the arm and (ii) suitable angle-dimensions for the links of the arm, where the angle-choices are limited to the values 0, ± π/2, and π. A geometric description of the dominant function for control is included. The same kinematic chains are surveyed for all possible parallel and right-angle arrangements of adjacent axes in the four links of the arm. Again utilizing screw theory, 160 robots are identified which do not posses full-cycle axis-dependence among some or all of the first five axes.

A Study on Determining Loops of Planar Kinematic Chains

1994 ◽  
Vol 208 (1) ◽  
pp. 59-63 ◽  
Author(s):  
W Li ◽  
Z Wang ◽  
H Li
Keyword(s):  
Kinematic Chain ◽  
Automatic Generation ◽  
Maximum Length ◽  
Small Length ◽  
Kinematic Chains ◽  
New Concepts ◽  
Large Length ◽  
First Time ◽  
Independent Loops

This paper presents for the first time a method for the automatic generation of independent and peripheral loops of planar kinematic chains. In order to implement this method, three laws are considered and some new concepts, for instance same-position link, similar loop, loop-link vector and loop-joint vector, are defined. By using structural matrices of planar kinematic chains, independent loops are generated in the order from those with small length to those with large length. Next, one peripheral loop with the maximum length is generated. Finally a loop-link matrix and a loop-joint matrix are obtained to express all independent loops and the peripheral loop in a planar kinematic chain.

Synthesis of a Rear Wheel Suspension Mechanism With Pure Rectilinear Motion

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Jing-Shan Zhao ◽  
Fulei Chu ◽  
Zhi-Jing Feng ◽  
Sheng Zhao
Keyword(s):  
Rigid Body ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Rear Wheel ◽  
Rectilinear Motion ◽  
Rear Suspension ◽  
Kinematic Chains ◽  
Redundant Constraint ◽  
Straight Line ◽  
Suspension Structure

This paper focuses on the synthesis of an independent suspension that can guide the wheel to track a straight line when moving up (jounce) and down (rebound). With displacement subgroups, it first synthesizes a rigid body guidance mechanism and verifies the result through screw theory. To simplify and optimize the loads of each kinematic chain of the knuckle, it investigates the static equations and ultimately synthesizes a symmetric redundant-constraint suspension structure, which could not only eliminate the shambling shocks induced by the jumping of wheels but also decrease the abrasion of tires. Theoretically, only one pair of noncoplanar kinematic chains is necessary to realize straight line guidance. However, a second pair of noncoplanar kinematic chains is particularly utilized to improve the load status of the links. Because of the redundant constraints induced by the suspension structures, the whole weight can be significantly reduced compared with the initial one. ADAMS simulations with a set of real parameters indicate that the rear suspension mechanism proposed in this paper can guide the wheel to follow a rectilinear locus during jounce and rebound. Therefore, this kind of independent suspension can improve the ride and handling properties of advanced vehicles.

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

2004 ◽  
Vol 126 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Screw Theory ◽  
General Procedure ◽  
Linear Equations ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Small Joint ◽  
Actuated Joints

A method is proposed for the type synthesis of 3-DOF (degree-of-freedom) translational parallel manipulators (TPMs) based on screw theory. The wrench systems of a translational parallel kinematic chain (TPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of TPMs. The type synthesis of legs for TPKCs, the type synthesis of TPKCs as well as the selection of actuated joints of TPMs are dealt with in sequence. An approach to derive the full-cycle mobility conditions for legs for TPKCs is proposed based on screw theory and the displacement analysis of serial kinematic chains undergoing small joint motions. In addition to the TPKCs proposed in the literature, TPKCs with inactive joints are synthesized. The phenomenon of dependent joint groups in a TPKC is revealed systematically. The validity condition of actuated joints of TPMs is also proposed. Finally, linear TPMs, which are TPMs whose forward displacement analysis can be performed by solving a set of linear equations, are also revealed.

Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain

2005 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Second Step ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Serial Chain ◽  
Parallel Kinematic

This paper presents a systematic approach for the mobility analysis of parallel mechanisms. The method is based on screw theory and the concept of equivalent serial chain. An equivalent serial kinematic chain of a k-legged PKC (parallel kinematic chain) is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. Using the proposed approach, the mobility analysis of a PKC is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step is dealt with based on screw theory. The second step is performed with the aid of the concept of equivalent serial chain and the types of multi-DOF overconstrained single-loop kinematic chains. The proposed approach is illustrated with several examples.

scholarly journals Virtual and Physical Prototyping of Reconfigurable Parallel Mechanisms with Single Actuation

2021 ◽  
Vol 11 (15) ◽  
pp. 7158
Author(s):  
Alexey Fomin ◽  
Daniil Petelin ◽  
Anton Antonov ◽  
Victor Glazunov ◽  
Marco Ceccarelli
Keyword(s):  
Computer Aided Design ◽  
Screw Theory ◽  
Complex Geometry ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Kinematic Chains ◽  
Physical Prototype ◽  
Detailed Computer ◽  
Aided Design

The paper presents novel models of reconfigurable parallel mechanisms (RPMs) with a single active degree-of-freedom (1-DOF). The mechanisms contain three to six identical kinematic chains, which provide three (for the tripod) to zero (for the hexapod) uncontrollable DOFs. Screw theory is applied to carry out mobility analysis and proves the existence of controllable and uncontrollable DOFs of these mechanisms. Each kinematic chain in the synthesized mechanisms consists of planar and spatial parts. Such a design provides them with reconfiguration capabilities even when the driving link is fixed. This allows reproduction of diverse output trajectories without using additional actuators. In this paper, the model of a mechanism with six kinematic chains (hexapod) has been virtually and physically prototyped. The designing and assembling algorithms are developed using the detailed computer-aided design (CAD) model, which was further used to carry out kinetostatic analysis considering complex geometry of mechanism elements and friction among all contacting surfaces of joints. The developed virtual prototype and its calculation data have been further applied to fabricate mechanism elements and assemble an actuated full-scale physical prototype for future testing.

An Approach to Determining the Unknown Twist/Wrench Subspaces of Lower Mobility Serial Kinematic Chains

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Tian Huang ◽  
Shuofei Yang ◽  
Manxin Wang ◽  
Tao Sun ◽  
Derek G. Chetwynd
Keyword(s):  
Linear Functional ◽  
Dual Space ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Dual Basis ◽  
Generalized Jacobian ◽  
Kinematic Chains ◽  
Essential Step ◽  
Effective Manner ◽  
Lower Mobility

Mainly drawing on screw theory and linear algebra, this paper presents an approach to determining the bases of three unknown twist and wrench subspaces of lower mobility serial kinematic chains, an essential step for kinematic and dynamic modeling of both serial and parallel manipulators. By taking the reciprocal product of a wrench on a twist as a linear functional, the underlying relationships among their subspaces are reviewed by means of the dual space and dual basis. Given the basis of a twist subspace of permissions, the causes of nonuniqueness in the bases of the other three subspaces are discussed in some depth. Driven by needs from engineering design, criteria, and a procedure are proposed that enable pragmatic, consistent bases of these subspaces to be determined in a meaningful, visualizable, and effective manner. Three typical examples are given to illustrate the entire process. Then, formulas are presented for the bases of the twist/wrench subspaces of a number of commonly used serial kinematic chains, which can readily be employed for the formulation of the generalized Jacobian of a variety of lower mobility parallel manipulators.

Structure Based Grading of Kinematic Chains

2014 ◽  
Vol 575 ◽  
pp. 501-506 ◽  
Author(s):  
Shubhashis Sanyal ◽  
G.S. Bedi
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Structural Differences ◽  
The Individual ◽  
Independent Loops

Kinematic chains differ due to the structural differences between them. The location of links, joints and loops differ in each kinematic chain to make it unique. Two similar kinematic chains will produce similar motion properties and hence are avoided. The performance of these kinematic chains also depends on the individual topology, i.e. the placement of its entities. In the present work an attempt has been made to compare a family of kinematic chains based on its structural properties. The method is based on identifying the chains structural property by using its JOINT LOOP connectivity table. Nomenclature J - Number of joints, F - Degree of freedom of the chain, N - Number of links, L - Number of basic loops (independent loops plus one peripheral loop).

Design of a Variable-Mobility Linkage Using the Bohemian Dome

2018 ◽  
Author(s):  
P. C. López-Custodio ◽  
J. S. Dai
Keyword(s):  
Configuration Space ◽  
Kinematic Chains ◽  
Paper Folding ◽  
First Time ◽  
The Relationship

The properties of the Bohemian dome are studied and it is found that for a particular type of Bohemian dome two different parameterizations based on the translation of circles can be obtained for the same surface, therefore, two different hybrid kinematic chains can be designed to generate the same Bohemian dome. These surface generators are reconfigurable and can generate two different surfaces each. Parameterizations for the secondary surfaces are obtained and studied. These hybrid kinematic chains are used to design a kinematotropic linkage with a total of 27 motion branches in its configuration space. The singularities in the configuration space are also determined using the properties of the surfaces. The resultant linkage offers an explanation of Wholhart’s queer-square linkage other than paper folding. The relationship between the properties of self-intersections in generated surfaces and the configuration space of the generator linkage is studied for the first time leading to the description of motion branches related to self-intersections of generated surfaces.

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