scholarly journals Analysis of Finite Self Motion and Finite Dwell in Closed-Loop Mechanisms and Parallel Manipulators

2001 ◽  
Author(s):  
Sandipan Bandyopadhyay ◽  
Ashitava Ghosal
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Constraints ◽  
Constraint Equations ◽  
First Order ◽  
Necessary And Sufficient Criteria ◽  
Necessary And Sufficient ◽  
Self Motion

Abstract In this paper, we present the necessary and sufficient criteria for finite self motion and finite dwell of the passive links of a parallel manipulator or a closed-loop mechanism. We study the first order properties of the constraint equations associated with the kinematic constraints inherent in a closed-loop mechanism or a parallel manipulator, and arrive at the criteria for the mechanism to gain a degree-of-freedom at a singular point of its workspace. By analyzing the second order properties of the constraint equations, we show that the gain of degree-of-freedom may lead to finite self motion of the passive links if certain configurational and architectural criteria are met. Special configurations and architecture may also lead to finite dwell of the passive links, and the criteria for the same has been derived. The results are illustrated with the help of several closed-loop mechanisms.

Integrated Kinematic Calibration for All the Parameters of a Planar 2DOF Redundantly Actuated Parallel Manipulator

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Chunshi Feng ◽  
Shuang Cong ◽  
Weiwei Shang
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Open Loop ◽  
Kinematic Calibration ◽  
Constraint Equations ◽  
Integrated Method ◽  
Uniqueness Of The Solution ◽  
Redundantly Actuated ◽  
Loop Constraint ◽  
Two Degree Of Freedom

In this paper, the kinematic calibration of a planar two-degree-of-freedom redundantly actuated parallel manipulator is studied without any assumption on parameters. A cost function based on closed-loop constraint equations is first formulated. Using plane geometry theory, we analyze the pose transformations that bring infinite solutions and present a kinematic calibration integrated of closed-loop and open-loop methods. In the integrated method, the closed-loop calibration solves all the solutions that fit the constraint equations, and the open-loop calibration guarantees the uniqueness of the solution. In the experiments, differential evolution is applied to compute the solution set, for its advantages in computing multi-optima. Experimental results show that all the parameters involved are calibrated with high accuracy.

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.

Motion Performance Analysis of Double-Cylinder Parallel Manipulators

2009 ◽  
Author(s):  
Hong Zhou ◽  
Shehu T. Alimi ◽  
Aravind Ravindranath ◽  
Hareesh Vepuri
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Critical Role ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
Two Degree Of Freedom

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

Kinematics of a partially decoupled 3R2T symmetrical parallel manipulator 3-RCRR

2008 ◽  
Vol 222 (2) ◽  
pp. 277-285 ◽  
Author(s):  
S-J Zhu ◽  
Z Huang ◽  
M Y Zhao
Keyword(s):  
Control System ◽  
Cervical Spine ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Short History ◽  
Translational Degree ◽  
And Performance

The 3R2T (three rotational and two independent translational degree of freedom (DoF)) symmetrical parallel manipulator may be adopted in bionics, for example, simulating the motion of a cervical spine based on their mobility property and performance close to isotropic limit. However, up to now, characteristics of this class of manipulators have not been well studied because of its short history. Hence, to study the feasibility of this class of manipulator for bionics, kinematics for 3-RCRR is analysed including position, singularity, velocity, and acceleration. Different from other 3R2T 5-DoF symmetrical parallel manipulators, the mobility of 3-RCRR is partially decoupled, which makes the realization of control system easier than in others.

Unified Solving Jacobian∕Hessian Matrices of Some Parallel Manipulators With n SPS Active Legs and a Passive Constrained Leg

2006 ◽  
Vol 129 (11) ◽  
pp. 1161-1169 ◽  
Author(s):  
Yi Lu ◽  
Bo Hu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Simple Approach ◽  
Spherical Joint ◽  
Load Bearing ◽  
Prismatic Joint ◽  
First Order ◽  
Partial Differentiation

Some parallel manipulators with n spherical joint-prismatic joint-spherical joint (SPS)-type active legs and a passive constrained leg possess a larger capability of load bearing and are simple in structure of the active leg. In this paper, a unified and simple approach is proposed for solving Jacobian∕Hessian matrices and inverse∕forward velocity and acceleration of this type of parallel manipulators. First, a general parallel manipulator with n SPS-type active legs and one passive constrained leg in various possible serial structure is synthesized, and some formulae for solving the poses of constrained force∕torque and active∕constrained force matrix are derived. Second, the formulae for solving extension of active legs, the auxiliary velocity∕acceleration equation are derived. Third, the formulae for solving inverse∕forward velocity and acceleration and a Jacobian matrix without the first-order partial differentiation and a Hessian matrix without the second-order partial differentiation are derived. Finally, the procedure is applied to three parallel manipulators with four and five SPS-type active legs and one passive constrained leg in different serial structures and to illustrate.

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

Workspace of Four-Degree-of-Freedom Manipulators

1996 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Harn-Jou Yeh
Keyword(s):  
Perturbation Technique ◽  
Underlying Mechanism ◽  
Degree Of Freedom ◽  
Parametric Surfaces ◽  
Singular Surfaces ◽  
End Effector ◽  
Serial Manipulators ◽  
Constraint Equations ◽  
First Order ◽  
Revolute Joints

Abstract An analytical method is presented to obtain all boundary surfaces to the accessible output set of four degree-of-freedom serial manipulators. The method is applicable to all manipulators that comprise combinations of prismatic and revolute joints. Position constraints of the end-effector of such mechanisms are formulated using the Denavit-Hartenberg representation. Examining the Jacobian of the underlying mechanism using a row-rank deficiency method yields sets of first-order singularities. These sets of singularities are substituted into the position constraint equations yielding parametric surfaces upon which the manipulator looses at least one degree of mobility. Singular curves are determined by intersecting singular surfaces. Due to the complexity of intersecting parametric singular surfaces, the resultant singular curves are numerically computed. Bifurcation points are identified and tangents are computed. Singular surfaces are partitioned into sub-surfaces that are studied for existence inside the accessible output set using a proposed perturbation technique. The result is a number of sub-surfaces that envelop the accessible output set. The theory presented is validated using a four-degree-of-freedom example.

Inverse and forward dynamics of N-3RPS manipulator with lockable joints

Robotica ◽  
2015 ◽  
Vol 34 (6) ◽  
pp. 1383-1402 ◽  
Author(s):  
Ali Taherifar ◽  
Hassan Salarieh ◽  
Aria Alasty ◽  
Mohammad Honarvar
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Closed Loop ◽  
Virtual Work ◽  
Forward Dynamics ◽  
Loop Structure ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Kinematic Constraints ◽  
Locking Mechanism

SUMMARYThe N-3 Revolute-Prismatic-Spherical (N-3RPS) manipulator is a kind of serial-parallel manipulator and has higher stiffness and accuracy compared with serial mechanisms, and a larger workspace compared with parallel mechanisms. The locking mechanism in each joint allows the manipulator to be controlled by only three wires. Modeling the dynamics of this manipulator presents an inherent complexity due to its closed-loop structure and kinematic constraints. In the first part of this paper, the inverse kinematics of the manipulator, which consists of position, velocity, and acceleration, is studied. In the second part, the inverse and forward dynamics of the manipulator is formulated based on the principle of virtual work and link Jacobian matrices. Finally, the numerical example is presented for some trajectories.

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.

Forward Displacement Analysis and Singularity Analysis of a Special 2-DOF 5R Spherical Parallel Manipulator

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type I ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Singular Configuration ◽  
Self Motion ◽  
Spherical Parallel Manipulator ◽  
Forward Displacement Analysis

This paper deals with the forward displacement analysis and singularity analysis of a special 2-DOF 5R spherical parallel manipulator, in which the angle between the axes of any two adjacent revolute joints is a right angle. An alternative formulation of the kinematic equations of the 5R spherical parallel manipulator is proposed. A formula is then derived to produce directly the unique current solution to the forward displacement analysis of the 5R spherical parallel manipulator. It will also be addressed to keep the spherical parallel manipulator in the same working mode and assembly mode by simply restraining the range of an input angle. Unlike other parallel manipulators, the 5R spherical parallel manipulator always undergoes self-motion in a type-II singular configuration, and the 3R leg of the 5R spherical parallel manipulator also always undergoes self-motion in a type-I singular configuration.

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