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 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.

Classification of 6-SPS Parallel Manipulators According to Their Components

2000 ◽  
Author(s):  
Xianwen Kong ◽  
Clément M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Type Synthesis ◽  
Forward Displacement ◽  
Quadratic Equations ◽  
Straight Lines ◽  
Forward Displacement Analysis

Abstract The complexity of the forward displacement analysis (FDA) of 6-SPS parallel manipulators1 varies to a great extent with the change of their geometric parameters. This paper presents a classification of the 6-SPS parallel manipulators according to their components. At first, we give the components for the 6-SPS parallel manipulator. A component refers to a part of the 6-SPS kinematic chain in which the number of actuators is equivalent to the degree of freedom. In addition to the commonly used rigid bodies, points and (straight) lines are also taken as elements of the components. Type synthesis of the 6-SPS parallel manipulators is then performed. The influence of the types of components on the maximal numbers of configurations and the degrees of the characteristic polynomials of the 6-SPS parallel manipulators is then revealed. The number of redundant sensors needed to reduce the FDA of 6-SPS parallel manipulators to the solution of several univariate quadratic equations in sequence based on the component method is also presented.

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.

Differential kinematics of parallel manipulators using Assur virtual chains

2009 ◽  
Vol 223 (7) ◽  
pp. 1697-1711 ◽  
Author(s):  
A Campos ◽  
R Guenther ◽  
D Martins
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Kinematic Constraints ◽  
Passive Joint ◽  
Planar Parallel Manipulator ◽  
Stewart Gough Platform ◽  
Homogeneous Linear

This article introduces the concept of Assur virtual chains and its applications in differential kinematics of parallel manipulators. Using Assur virtual chains, the differential kinematics has a simple matricial formulation and the choice between direct and inverse kinematics is reduced to select primary variables in a homogeneous linear system. Assur virtual chains are also useful for obtaining information about the relative movements or to imposing particular kinematic constraints between two links of a kinematic chain. Additionally, a new systematic algorithm is established to analytically eliminate passive joint velocities and calculate the Jacobian matrices. This elimination approach is based on screw theory concepts such as twist, wrench, and reciprocity; also, graph theory is used for kinematic chain representation. At the end of the article, the method is applied to a 3RRR planar parallel manipulator and a general universal-prismatic-spheric Stewart—Gough platform.

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.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

1998 ◽  
Author(s):  
Xian-Wen Kong
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Dual Solutions ◽  
Fourth Degree ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

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.

An efficient method for the dynamic modeling and analysis of Stewart parallel manipulator based on the screw theory

2019 ◽  
Vol 234 (3) ◽  
pp. 808-821
Author(s):  
Yulei Hou ◽  
Guoxing Zhang ◽  
Daxing Zeng
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Force Balance ◽  
Constraint Matrix ◽  
Scheme Design ◽  
Control Scheme

Dynamic modeling serves as the fundamental basis for dynamic performance analysis and is an essential aspect of the control scheme design of parallel manipulators. This report presents a concise and efficient solution to the dynamics of Stewart parallel manipulators based on the screw theory. The initial pose of these manipulators is described. Then the pose matrix of each link of the Stewart parallel mechanism is obtained using an inverse kinematics solution and an exponential product formula. Considering the constraint relationship between joints, the constraint matrix of the Stewart parallel manipulator is deduced. In addition, the Jacobian matrix and the twist of each link are obtained. Moreover, by deriving the differential form of the constraint matrix, the spatial acceleration of each link is obtained. Based on the force balance relationship of each link, the inverse dynamics and the general form of the dynamic model of the Stewart parallel manipulator is established and the process of inverse dynamics is summarized. The dynamic model is then verified via dynamic simulation using the ADAMS software. A numerical example is considered to demonstrate the feasibility and effectiveness of this model. The proposed dynamic modeling approach serves as a fundamental basis for structural optimization and control scheme design of the Stewart parallel manipulators.

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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