Analysis of kinematics and solution of active/constrained forces of asymmetric 2UPU+X parallel manipulators

2006 ◽  
Vol 220 (12) ◽  
pp. 1819-1830 ◽  
Author(s):  
Y Lu ◽  
B Hu
Keyword(s):  
Parallel Manipulators ◽  
Transformation Matrix ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
New Family ◽  
Kinematic Characteristics ◽  
Force Transformation

A new family of asymmetric 2UPU+X parallel manipulators is proposed. It includes two identical UPU-type active legs and one X-type active leg which may be various five-degree-of-freedom serial mechanisms. First, their common kinematic characteristics and singularity are analysed, and some common formulae for analysing inverse-forward kinematics, solving active/constrained force transformation matrix and active/constrained forces, are derived. Second, three asymmetric 3-UPU, 2UPU + SPR, and 2UPU + RPRU parallel manipulators are created, their kinematics and singularity are analysed, and their active/constrained forces are solved.

scholarly journals Kinematic Analysis Of Tricept Parallel Manipulator

2012 ◽  
Vol 12 (5) ◽  
Author(s):  
Mir Amin Hosseini ◽  
Hamid-Reza Mohammadi Daniali
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Forward Kinematics ◽  
Jacobian Matrices ◽  
Moving Platforms ◽  
Workspace Optimization

Parallel manipulators consist of fixed and moving platforms connected to each other with some actuated links. They have some significant advantages over their serial counterparts. While, they suffer from relatively small workspaces, complex kinematics relations and highly singular points within their workspaces. In this paper, forward kinematics of Tricept parallel manipulator is solved analytically and its workspace optimization is performed. This parallel manipulator has a complex degree of freedom, therefore leads to dimensional in-homogeneous Jacobian matrices. Thus, we divide some entries of the Jacobian by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. Moreover, its workspace is parameterized using some design parameters. Then, using GA method, the workspace is optimized subjects to some geometric constraints. Finally, dexterity of the design is evaluated. Keywords- Kinematic, Workspace, Singularity, TriceptABSTRAK - Manipulator selari terdiri daripada platform tetap dan bergerak yang bersambung antara satu sama lain dengan beberapa pautan bergerak. Manipulator selari mempunyai beberapa kebaikan tertentu dibandingkan dengan yang bersamaan dengannya. Walaupun ia mempunyai ruang kerja yang sempit, hubungan kinematik kompleks dan titik tunggal tinggi dalam linkungan ruang kerjanya. Dalam kajian ini, kinematik ke hadapan manipulator selari Tricept diselesaikan secara analisa dan pengoptimuman ruang kerja dijalankan. Manipulator selari ini mempunyai darjah kebebasan yang kompleks, yang menyebabkan ia mendorong kepada kehomogenan dimensi matriks Jacobian. Catatan Jacobian dibahagikan kepada unit panjang, dimana ia menghasilkan Jacobian baru yang homogen dimensinya. Tambahan, ruang kerjanya diparameterkan dengan menggunakan beberapa parameter reka bentuk. Kemudian, dengan kaedah GA, ruang kerja mengoptimakan subjek kepada beberapa kekangan geometrik. Akhirnya, kecakatan reka bentuk dinilaikan.Keywords- Kinematic, Workspace, Singularity, Tricept

Forward Kinematics of 3-GPR Planar Parallel Manipulators With Circular Rolling Contact Joints

2003 ◽  
Author(s):  
Curtis L. Collins
Keyword(s):  
Relative Motion ◽  
Parallel Manipulators ◽  
Solution Procedure ◽  
Rolling Contact ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Prismatic Joint ◽  
Forward Kinematic ◽  
Planar Parallel Manipulators ◽  
Circular Contact

In this work, we investigate the geometry and position kinematics of planar parallel manipulators composed of three GPR serial sub-chains, where G denotes a rolling contact, or geared joint, P denotes a prismatic joint, and R denotes a revolute joint. The rolling contact joints provide a passive one degree-of-freedom relative motion between the base and the prismatic links. It is shown, both theoretically and numerically, that when all the G-joints have equal circular contact profiles, there are at most 48 real forward kinematic solutions when the P joints are actuated. The solution procedure is general and can be used to predict and solve for the kinematics solutions of 3-GPR manipulators with any combination of rational contact ratios.

Singularity and Controllability Analysis of Parallel Manipulators

1998 ◽  
Author(s):  
Prasun Choudhury ◽  
Ashitava Ghosal
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Transformation Matrix ◽  
Constraint Forces ◽  
Numerical Examples ◽  
Cartesian Space ◽  
Force Transformation

Abstract This paper presents a study of kinematic and force singularities and their relationship to the controllability of planar and spatial parallel manipulators. Parallel manipulators are classified according to their degrees of freedom, number of output Cartesian variables used to describe their motion and the number of actuated joint inputs. The singularities in the workspace of a parallel manipulator are studied by considering the force transformation matrix which maps the forces and torques in joint space to output forces and torques in Cartesian space. The uncontrollable regions in the workspace of the parallel manipulator are obtained by deriving the equations of motion in terms of Cartesian variables and by using techniques from Lie Algebra. We show that when the number of actuated joint inputs is equal to the number of output Cartesian variables, and the force transformation matrix loses rank, the parallel manipulator is uncontrollable. For the case of manipulators where the number of joint inputs is less than the number of output Cartesian variables, if the constraint forces and torques (represented by the Lagrange multipliers) become infinite, the force transformation matrix loses rank. Finally, we show that the singular and uncontrollable regions in the workspace of a parallel manipulator can be reduced by adding redundant joint actuators and links. The results are illustrated with the help of numerical examples where we plot the singular and uncontrollable regions of parallel manipulators belonging to the above mentioned classes.

A unified method to find active forces and passive wrench of some parallel manipulators with n SPS active legs and a passive leg

2007 ◽  
Vol 221 (4) ◽  
pp. 467-478 ◽  
Author(s):  
Y Lu ◽  
B Hu
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulators ◽  
Transformation Matrix ◽  
Analysis Approach ◽  
Active Force ◽  
Force Transformation ◽  
Unified Method

A unified analysis approach is proposed for solving the active force and the passive wrench of some parallel manipulators with n SPS-type active legs and an unactuated passive leg. Firstly, some mathematical formulae for solving the force transformation matrix and active force and passive wrench are derived, and many possible types of the unactuated passive constrained legs are synthesized. Secondly, three parallel manipulators with three to five SPS-type active legs and a different passive leg are presented to illustrate as how to solve their inverse kinematics, force matrix, active forces, and passive wrench, and singularity by using the force matrix. Thirdly, some examples are given, and solving results have been verified by the simulation mechanism approach.

A new family of spatial 3-DOF parallel manipulators with two translational and one rotational DOFs

Robotica ◽  
2009 ◽  
Vol 27 (2) ◽  
pp. 241-247 ◽  
Author(s):  
Xin-Jun Liu ◽  
Jinsong Wang ◽  
Chao Wu ◽  
Jongwon Kim
Keyword(s):  
Energy Saving ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
New Family ◽  
Very High

SUMMARYThis paper proposes a new family of spatial 3-DOF (degree of freedom) parallel manipulators with two translational and one rotational DOFs. The manipulators in this family are the variations of the parallel manipulators, which are capable of very high rotational capability, introduced by X.-J. Liu, J. Wang, and G. Pritschow (“A new family of spatial 3-DoF fully parallel manipulators with high rotational capability,” Mech. Mach. Theory40(4), 475–494, 2005). However, compared with those old manipulators, the new parallel manipulators proposed here have the advantages of simpler kinematics and structure, easier manufacturing, and energy saving.

scholarly journals Degeneracy Study of the Forward Kinematics of Planar 3-RP̱R Parallel Manipulators

2006 ◽  
Vol 129 (12) ◽  
pp. 1265-1268 ◽  
Author(s):  
P. Wenger ◽  
D. Chablat ◽  
M. Zein
Keyword(s):  
Characteristic Polynomial ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Industrial Applications ◽  
Forward Kinematics ◽  
Double Root ◽  
Degree Polynomial ◽  
New Family ◽  
Planar Manipulators ◽  
First Time

This paper investigates two situations in which the forward kinematics of planar 3-RP̱R parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables ρ1, ρ2, and ρ3 satisfy a certain relationship. This degeneracy yields a double root of the characteristic polynomial in t=tan(φ∕2), which could be erroneously interpreted as two coalesce assembly modes. However, unlike what arises in nondegenerate cases, this double root yields two sets of solutions for the position coordinates (x,y) of the platform. In the second situation, we show that the forward kinematics degenerates over the whole joint space if the base and platform triangles are congruent and the platform triangle is rotated by 180deg about one of its sides. For these “degenerate” manipulators, which are defined here for the first time, the forward kinematics is reduced to the solution of a third-degree polynomial and a quadratic in sequence. Such manipulators constitute, in turn, a new family of analytic planar manipulators that would be more suitable for industrial applications.

A New Family of Bricard-Derived Deployable Mechanisms

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Hailin Huang ◽  
Bing Li ◽  
Jianyang Zhu ◽  
Xiaozhi Qi
Keyword(s):  
Large Volume ◽  
Computer Aided Design ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
New Family ◽  
Revolute Joints ◽  
Computer Aided ◽  
Cad Models ◽  
Aided Design

This paper proposes a new family of single degree of freedom (DOF) deployable mechanisms derived from the threefold-symmetric deployable Bricard mechanism. The mobility and geometry of original threefold-symmetric deployable Bricard mechanism is first described, from the mobility characterstic of this mechanism, we show that three alternate revolute joints can be replaced by a class of single DOF deployable mechanisms without changing the single mobility characteristic of the resultant mechanisms, therefore leading to a new family of Bricard-derived deployable mechanisms. The computer-aided design (CAD) models are used to demonstrate these derived novel mechanisms. All these mechanisms can be used as the basic modules for constructing large volume deployable mechanisms.

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.

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