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.

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.

Type Synthesis of 3-DOF PPR Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain

2004 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Motion Patterns ◽  
Kinematic Chains ◽  
Serial Robots ◽  
Prismatic Joints ◽  
Parallel Kinematic ◽  
Actuated Joints ◽  
Selection Of

PPR-PMs (parallel manipulators) are the parallel counterparts of the 3-DOF PPR serial robots, which are composed of two P (prismatic) joints and one R (revolute) joint. For a PPR-PM, the moving platform can rotate arbitrarily about an axis undergoing a planar translation. This paper deals with the type synthesis of 3-DOF PPR-PMs. At first, virtual chains are introduced to represent the motion patterns of 3-DOF motions and relevant results from screw theory are recalled. A method is then proposed for the type synthesis of 3-DOF PPR-PMs. Using the proposed approach, the type synthesis of 3-DOF PPR-PMs is performed in three steps, namely, the type synthesis of legs for PPR-PKCs (parallel kinematic chains), the type synthesis of PPR-PKCs, and the selection of actuated joints of PPR-PMs. The three steps are dealt with in detail consequently. The characteristics of the proposed approach is that the type synthesis of legs for PPR-PKCs is reduced to the type synthesis of 3-DOF overconstrained single-loop kinematic chains and thus easy to perform. In addition to all the 3-DOF PPR-PKCs and 3-DOF PPR-PMs proposed in the literature, a number of new 3-DOF PPR-PKCs and 3-DOF PPR-PMs are identified. It is also found that there are no PPR-PMs with identical types of legs.

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.

Synthesis of 2T1R Decoupled Parallel Manipulators

2011 ◽  
Vol 308-310 ◽  
pp. 2025-2030 ◽  
Author(s):  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Da Xing Zeng ◽  
Ruo Song Wang
Keyword(s):  
Screw Theory ◽  
Control Design ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Step Procedure ◽  
Nonlinear Relation ◽  
Three Degree Of Freedom

For the general parallel mechanisms(PMS), since the coupling between kinematic chains, the nonlinear relation between the input and output is presented, which have led to difficulty in the trajectory planning and precision control. Design of motion decoupled parallel mechanisms(DPMS) has become a good new topic in this area and has captured researcher's attention. In this work, the approach to a synthesis of three degree-of-freedom(3-DOF) DPMS is considered based on screw theory and motion synthesis ideas. Criterions for type synthesis of the branches for DPMS is established according to the twist screw system of the limbs, which assures the decoupling in each limb. Then a six-step procedure is presented for the type synthesis of 2T1R decoupled mechanisms.

Type Synthesis of Uncoupled 2T2R Parallel Manipulators

2012 ◽  
Author(s):  
Yanbin Zhang ◽  
Kwun-lon Ting
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Control Design ◽  
Parallel Manipulators ◽  
Velocity Space ◽  
Type Synthesis ◽  
Systematic Method ◽  
Structure Synthesis ◽  
Hybrid Manipulator ◽  
Actuated Joints

This paper presents a simple and systematic method for type synthesis of four-degree-of-freedom uncoupled parallel manipulators with two-translational and two-rotational (2T2R) motion components. Based on the concept of hybrid manipulator, one uncoupled 2T2R hybrid manipulator, which is composed of one full-isotropic planar 2T1R parallel manipulator and one revolute joint in serial assembly, is designed first. Then the structure synthesis of the fourth leg of 2T2R parallel manipulator is performed in terms of the reciprocal screw theory. Finally, the type synthesis of uncoupled 2T2R parallel manipulators is realized by combining the uncoupled 2T2R hybrid manipulator and one of the synthesized fourth legs. The Jacobian of the uncoupled 2T2R parallel manipulator is a 4×4 diagonal matrix. Therefore, there exists a one-to-one correspondence between the input velocity space of the actuated joints and the output velocity space of the moving platform. Moreover, both the control design and the path planning of these proposed manipulators are very simple.

Synthesis of Two-Degree-of-Freedom Rotational Decoupled Manipulators of a 2R-Type Branch

2013 ◽  
Vol 284-287 ◽  
pp. 1929-1935
Author(s):  
Da Xing Zeng ◽  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Yi Tong Zhang
Keyword(s):  
Trajectory Planning ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Parallel Kinematic ◽  
Branch Type ◽  
Two Degree Of Freedom

Strong coupling is one of the prominent features of the general parallel mechanisms(Par. Mec.), which has led to difficulty in the trajectory planning and precision control. To solve this problem, the designing of motion decoupled parallel mechanisms(Dec. Par. Mec.) has become a hot topic. This paper, based on the work achieved in our pre-papers, is to make an improvement on the criterion for a branch type synthesis of the rotational decoupled parallel mechanisms(Rot. Dec. Par. Mec.), which ensures the decoupling of the rotations in each limb. This paper focuses on a type synthesis of the decoupled parallel mechanisms with two degree of freedoms (DOFs). Decoupled parallel manipulators with two parallel kinematic chains, one of which is of type 2R(R represents rotation), are taken into consideration in this paper. A large number of novel decoupled architectures are already obtained, some of which have got an application for a China Patent. What has been done in this paper is carried out by means of the screw theory, which has effectively avoided complex equations by synthesis.

Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain

2005 ◽  
Vol 127 (6) ◽  
pp. 1113-1121 ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Motion Patterns ◽  
Kinematic Chains ◽  
Serial Robots ◽  
Application Potential ◽  
Parallel Kinematic ◽  
Moving Platform ◽  
Identical Type

PPR-equivalent parallel manipulators (PMs) are a class of 3-DOF PMs with great application potential. They are indeed the parallel counterparts of the 3-DOF PPR serial robots, in which the moving platform can rotate arbitrarily about an axis undergoing a planar translation. This paper deals with the type synthesis of 3-DOF PPR-equivalent PMs. At first, virtual chains are introduced to represent the motion patterns of 3-DOF motions and relevant results from screw theory are recalled. A method is then proposed for the type synthesis of 3-DOF PPR-equivalent PMs. Using the proposed approach, the type synthesis of 3-DOF PPR-equivalent PMs is performed in three steps. In addition to all the 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs proposed in the literature, a number of new 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs are identified. It is also found that there are no PPR-equivalent PMs with identical type of legs. The type synthesis of PPR-equivalent PMs is well solved using the proposed approach. The characteristic of the proposed approach is that the type synthesis of PPR-equivalent parallel kinematic chains is reduced to the type synthesis of 3-DOF single-loop kinematic chains and thus easy to perform.

Structure Types Synthesis of Multiloop Spatial Kinematic Chains With General Variable Constraints

1998 ◽  
Author(s):  
Yufeng Luo ◽  
Tingli Yang ◽  
Ali Seireg
Keyword(s):  
Kinematic Chain ◽  
Structure Type ◽  
Type Synthesis ◽  
Kinematic Chains ◽  
Systematic Procedure ◽  
Independent Loops

Abstract A systematic procedure is presented for the structure type synthesis of multiloop spatial kinematic chains with general variable constraints in this paper. The parameters and the structure types of the contracted graphs and the branch chains used to synthesize such kinematic chains are given for kinematic chains with up to four independent loops. The assignments for the constraints values of all the loops in a kinematic chain are discussed. Using these as the basis, the structure types of the multiloop spatial kinematic chains with hybrid constraints could be synthesized.

Evaluation of Topological Properties of Parallel Manipulators Based on the Topological Characteristic Indexes

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1381-1399 ◽  
Author(s):  
Huiping Shen ◽  
Ting-Li Yang ◽  
Ju Li ◽  
Dan Zhang ◽  
Jiaming Deng ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Design Guidelines ◽  
Design Knowledge ◽  
Topological Properties ◽  
Topological Characteristic ◽  
Actuated Joints ◽  
Selection Of

SUMMARYThe topological structure of a parallel manipulator (PM) determines its intrinsic topological properties (TPs). The TPs further determine essential kinematic and dynamic properties of the mechanism. TPs can be expressed through topological characteristics indexes (TCI). Therefore, defining a set of TCIs is an important issue to evaluate the TPs of PMs. This article addresses the evaluation of topological properties (ETP) of PMs based on TCI. A general and effective ETP method for PMs is proposed. Firstly, 12 TCIs are proposed, including 8 quantitative TCIs, that is, position and orientation characteristics sets (POC), dimension of the POC set, degrees of freedom (DOF), number of independent displacement equations, types and number of an Assur kinematic chain (AKC), coupling degrees of the AKCs, degrees of redundancy and the number of overs; as well as 4 qualitative TCIs, that is, selection of actuated joints, identification of inactive joints, DOF type and Input–Output motion decoupling. Secondly, the ETP method is illustrated by evaluating some well-known PMs including the Delta, Tricept, Exechon, Z3, H4 and the Gough–Stewart platform manipulators, as well as 28 other typical PMs. Via the ETP analysis of these mechanisms also some valuable design knowledge is derived and guidelines for the design of PMs are established. Finally, a 5-DOF decoupled hybrid spraying robot is developed by applying the design knowledge and the design guidelines derived from the ETP analysis.

Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator

2010 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment Gosselin ◽  
James M. Ritchie
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Alternative Formulation ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Actuated Joints ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators — leg actuation singularity — is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.

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