Kinematics and dynamics of a six-degree-of-freedom parallel manipulator with revolute legs

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 385-394 ◽  
Author(s):  
Kourosh E. Zanganeh ◽  
Rosario Sinatra ◽  
Jorge Angeles
Keyword(s):  
Computer Simulation ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Displacement Velocity ◽  
Kinematics And Dynamics ◽  
Cartesian Space ◽  
Moving Platforms ◽  
Proposed Model ◽  
Six Degree Of Freedom

This paper presents the kinematics and dynamics of a six-degree-of-freedom platform-type parallel manipulator with six revolute legs, i.e. each leg consists of two links that are connected by a revolute joint. Moreover, each leg is connected, in turn, to the base and moving platforms by means of universal and spherical joints, respectively. We first introduce a kinematic model for the manipulator under study. Then, this model is used to derive the kinematics relations of the manipulator at the displacement, velocity and acceleration levels. Based on the proposed model, we develop the dynamics equations of the manipulator using the method of the natural orthogonal complement. The implementation of the model is illustrated by computer simulation and numerical results are presented for a sample trajectory in the Cartesian space.

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.

Stiffness-based trajectory planning of a 6-DOF cable-driven parallel manipulator

2016 ◽  
Vol 231 (21) ◽  
pp. 3999-4011 ◽  
Author(s):  
Wenjia Zhang ◽  
Weiwei Shang ◽  
Bin Zhang ◽  
Fei Zhang ◽  
Shuang Cong
Keyword(s):  
Velocity Profile ◽  
Trajectory Planning ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Performance Indices ◽  
Curved Trajectories ◽  
Quintic Polynomial ◽  
Point To Point ◽  
Six Degree Of Freedom

The stiffness of the cable-driven parallel manipulator is usually poor because of the cable flexibility, and the existing methods on trajectory planning mainly take the minimum time and the optimal energy into account, not the stiffness. To solve it, the effects of different trajectories on stiffness are studied for a six degree-of-freedom cable-driven parallel manipulator, according to the kinematic model and the dynamic model. The condition number and the minimum eigenvalue of the dimensionally homogeneous stiffness matrix are selected as performance indices to analyze the stiffness changes during the motion. The simulation experiments are implemented on a six degree-of-freedom cable-driven parallel manipulator, to study the stiffness of three different trajectory planning approaches such as S-type velocity profile, quintic polynomial, and trigonometric function. The accelerations of different methods are analyzed, and the stiffness performances for the methods are compared after planning the point-to-point straight and the curved trajectories. The simulation results indicate that the quintic polynomial and S-type velocity profile have the optimal performance to keep the stiffness stable during the motion control and the travel time of the quintic polynomial can be optimized sufficiently while keeping stable.

Determination of the Workspace of 6-DOF Parallel Manipulators

1990 ◽  
Vol 112 (3) ◽  
pp. 331-336 ◽  
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

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 in 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.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

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

scholarly journals A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 357
Author(s):  
Fengxuan Zhang ◽  
Silu Chen ◽  
Yongyi He ◽  
Guoyun Ye ◽  
Chi Zhang ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Kinematic Model ◽  
Calibration Method ◽  
Error Modeling ◽  
Degree Of Freedom ◽  
Least Square ◽  
Kinematic Calibration ◽  
Recursive Least Square ◽  
Local Product ◽  
Branched Chain

This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

Sign in / Sign up

Export Citation Format

Share Document