Kinematics Analysis of Some Linear Legs With Different Structures for Limited-DOF Parallel Manipulators

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Yi Lu ◽  
Bo Hu ◽  
Jianda Han ◽  
Jianping Yu
Keyword(s):  
Angular Velocity ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Dynamics Analysis ◽  
Kinematics Analysis ◽  
Challenging Issue ◽  
Piston Cylinder ◽  
Limited Degree

To solve the velocity and acceleration of legs with different structures is a fundamental and challenging issue for dynamics analysis of parallel manipulators (PMs). In this paper, the kinematics of linear legs with different structures for limited-degree of freedom (DOF) PMs is studied. First, based on kinematics/statics of general limited-DOF PM, the formulas are derived for solving the angular velocity/acceleration of some linear legs with different structures. Second, the velocity and acceleration of the piston/cylinder in the legs are represented by velocity and acceleration of platform in PM. Finally, the solving procedures are illustrated by applying this approach to a 4DOF PM.

Solving active wrench of limited-degree of freedom parallel manipulators based on translational/rotational Jacobian matrices

2009 ◽  
Vol 223 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Y Lu ◽  
B Hu ◽  
J Yu
Keyword(s):  
Virtual Work ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Principle Of Virtual Work ◽  
Jacobian Matrices ◽  
Limited Degree

A methodology is proposed for unified solving active wrench of the limited-degree of freedom (DOF) parallel manipulators (PMs). First, the geometric constraints and the inverse displacement kinematics are analysed. Second, the formulae for unified solving the inverse/forward velocity and the translational/rotational Jacobian matrices and inverse/forward Jacobian matrices are derived. Third, the analytic formulae for unified solving the active wrench of limited-DOF PMs are derived based on the principle of virtual work. Finally, a 3-DOF PM with linear/rotational active legs is presented to illustrate the use of the methodology.

scholarly journals Singularity and branch identification of a 2 degree-of-freedom (DOF) seven-bar spherical parallel manipulator

2020 ◽  
Vol 11 (2) ◽  
pp. 381-393
Author(s):  
Liangyi Nie ◽  
Huafeng Ding ◽  
Andrés Kecskeméthy ◽  
Jinqiang Gan ◽  
Jun Wang ◽  
...  
Keyword(s):  
Parallel Manipulators ◽  
Industrial Applications ◽  
Degree Of Freedom ◽  
Loop Structure ◽  
Branch Points ◽  
Kinematics Analysis ◽  
Joint Rotation ◽  
Speed Accuracy ◽  
Spherical Parallel Manipulator ◽  
Reaction Speed

Abstract. Spherical parallel manipulators (SPMs) have a great potential for industrial applications of robot wrists, camera-orientating devices, and even sensors because of their special structure. However, increasing with the number of links, the kinematics analysis of the complex SPMs is formidable. The main contribution of this paper is to present a kind of 2 degree-of-freedom (DOF) seven-bar SPM containing two five-bar spherical loops, which has the advantages of high reaction speed, accuracy rating, and rigidity. And based on the unusual actuated choices and symmetrical loop structure, an approach is provided to identify singularities and branches of this kind of 2 DOF seven-bar SPM according to three following steps. Firstly, loop equations of the two five-bar spherical loops, which include all the kinematic characteristics of this SPM, are established with joint rotation and side rotation. Secondly, branch graphs are obtained by Maple based on the discriminants of loop equations and the concept of joint rotation space (JRS). Then, singularities are directly determined by the singular boundaries of the branch graphs, and branches are easily identified by the overlapping areas of JRS of two five-bar spherical loops. Finally, this paper distinguishes two types of branches of this SPM according to whether branch points exist to decouple the kinematics, which can be used for different performance applications. The proposed method is visual and offers geometric insights into understanding the formation of mobility using branch graphs. At the end of this paper, two examples are employed to illustrate the proposed method.

Synthesis and Analysis of a Group of 3-Degree-of-Freedom Partially Decoupled Parallel Manipulators

2004 ◽  
Vol 126 (2) ◽  
pp. 301-306 ◽  
Author(s):  
Qiong Jin ◽  
Ting-Li Yang
Keyword(s):  
Topological Structure ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Structural Synthesis ◽  
Real Time Control ◽  
Structure Characteristics ◽  
Time Control ◽  
Internal Relationship

The kinematics decoupling for parallel manipulators is studied in this paper. Based on the topological structure characteristics of parallel mechanisms, the internal relationship between kinematics decoupling and basic kinematics chains is revealed, and the basic principle for structural synthesis of topologically decoupled mechanisms is put forward. Using this theory, a group of 3 degree-of-freedom (DOF) partially decoupled manipulators are synthesized. The expected kinematic outputs of these manipulators are 1-DOF translation and 2-DOF rotation, and motions along or about undesired directions do not exist. The kinematics analysis of a newly synthesized manipulator is discussed and the results indicate that the decoupling property of these architectures makes possible reaching real time control and path planning of parallel manipulators.

Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Parametric Design ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Arbitrary Base ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

scholarly journals Kinematics of a screw linkage

2021 ◽  
Vol 3 (12) ◽  
Author(s):  
Jing-Shan Zhao ◽  
Song-Tao Wei ◽  
Junjie Ji
Keyword(s):  
Angular Velocity ◽  
Linear Velocity ◽  
Kinematics Analysis ◽  
First Order ◽  
Definition Of

AbstractThis paper proposes a kinematics methodology in twist coordinates for screw linkages. Based on the definition of a twist, both the angular velocity of a link and the linear velocity of a point on it may be explicitly represented in twist coordinates. Through integration on the twist solution numerically or analytically, we may obtain the displacements. By differential or numerical differential interpolation of the twist, we can find the accelerations of the link. The most outstanding advantage of this kinematic algorithm is that only the numerical differential interpolation of the first order is required to calculate the acceleration while only the first order integration of the twist is enough to compute the displacement. This merit makes it particularly fit for developing programmes to accomplish the kinematics analysis of a spatial linkage.

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Workspace optimization of a class of zero-torsion parallel wrists

Robotica ◽  
2018 ◽  
Vol 37 (7) ◽  
pp. 1174-1189 ◽  
Author(s):  
Yuanqing Wu ◽  
Marco Carricato
Keyword(s):  
Tilt Angle ◽  
General Class ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Properties ◽  
Large Rotation ◽  
Workspace Optimization ◽  
Two Degree Of Freedom

SUMMARYWe present singularity-free workspace optimization of a class of two-degree-of-freedom (2-DoF) parallel wrists with large rotation range capability. The wrists in consideration are kinematically equivalent to two families of 2-DoF homokinetic couplings. The first family comprises fully parallel wrists with N (N ≥ 3) double-universal ($\mathcal{UU}$) legs. The second family comprises spherical N-$\mathcal{UU}$ parallel wrists with interconnecting revolute ($\mathcal{R}$) joints. Both families belong to the more general class of zero-torsion parallel manipulators, and are, therefore, collectively referred to as zero-torsion wrists (ZTWs). We carry out a unified singularity-free workspace optimization by utilizing geometric properties of zero-torsion motion manifolds. Our work may serve as a conceptual guide to the design of ZTWs for large tilt-angle applications.

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