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.

A Novel Parallel Mechanism With 3-RRUR Legs

2007 ◽  
Author(s):  
Yanwen Li ◽  
Yueyue Zhang ◽  
Lumin Wang ◽  
Zhen Huang
Keyword(s):  
Machine Tools ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Symmetrical Structure ◽  
Forward Kinematic ◽  
Accumulated Error

This paper investigates a novel 4-DOF 3-RRUR parallel manipulator, the number and the characteristics of its degrees of freedom are determined firstly, the rational input plan and the invert and forward kinematic solutions are carried out then. The corresponding numeral example of the forward kinematics is given. This type of parallel manipulators has a symmetrical structure, less accumulated error, and can be used to construct virtual-axis machine tools. The analysis in this paper will play an important role in promoting the application of such manipulators.

Forward Kinematics of Nonpolyhedral Parallel Manipulators

1993 ◽  
Vol 115 (4) ◽  
pp. 938-940 ◽  
Author(s):  
Jean-Pierre Merlet
Keyword(s):  
Symmetry Axis ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Forward Kinematic

Forward kinematics has been studied for polyhedral parallel manipulators. We present here an algorithm for the forward kinematic of nonpolyhedral manipulators the plates of which have a symmetry axis. We show that there will be at most 352 possible solutions and exhibit a configuration with eight solutions.

Forward Kinematics Solution Distribution and Analytic Singularity-Free Workspace of Linear-Actuated Symmetrical Spherical Parallel Manipulators

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal Seneviratne
Keyword(s):  
Coordinate System ◽  
Optimization Design ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Forward Kinematics ◽  
Kinematics Model ◽  
Analytic Singularity ◽  
Dynamics And Control ◽  
Rotation Motion ◽  
Forward Kinematic

This paper presents a new kinematics model for linear-actuated symmetrical spherical parallel manipulators (LASSPMs) which are commonly used considering their symmetrical kinematics and dynamics properties. The model has significant advantages in solving the forward kinematic equations, and in analytically obtaining singularity loci and the singularity-free workspace. The Cayley formula, including the three Rodriguez–Hamilton parameters from a general rotation matrix, is provided and used in describing the rotation motion and geometric constraints of LASSPMs. Analytical solutions of the forward kinematic equations are obtained. Then singularity loci are derived, and represented in a new coordinate system with the three Rodriguez–Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are illustrated and forward kinematics (FK) solution distribution in the singularity-free zones is discussed. Based on this analysis, unique forward kinematic solutions of LASSPMs can be determined. By using Cayley formula, analytical workspace boundaries are expressed, based on a given mechanism structure and input actuation limits. The singularity-free workspace is demonstrated in the proposed coordinate system. The work gives a systematic method in modeling kinematics, singularity and workspace analysis which provides new optimization design index and a simpler kinematics model for dynamics and control of LASSPMs.

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

Static Balancing of Spatial and Planar Parallel Manipulators With Prismatic Actuators

1998 ◽  
Author(s):  
Marc Leblond ◽  
Clément M. Gosselin
Keyword(s):  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Static Balancing ◽  
Inertial Parameters ◽  
Dimensional Parameters ◽  
Balancing Conditions ◽  
Static Conditions ◽  
Planar Parallel Manipulators

Abstract In this paper, the static balancing of existing spatial and planar parallel manipulators by the addition of balancing elements is addressed. Static balancing is defined here as the set of conditions on manipulator dimensional and inertial parameters which, when satisfied, ensure that the weight of the links does not produce any force (or torque) at the actuators for any configuration of the manipulator, under static conditions. These conditions are derived here for spatial six-degree-of-freedom parallel manipulators and it is shown that planar three-degree-of-freedom parallel manipulators can be treated as a particular case of the spatial 6-dof mechanisms. The static balancing conditions associated with planar mechanisms can therefore easily be found, but are not given here because of space limitations. A brief geometric interpretation of the balancing conditions which are associated with statically balanced spatial mechanisms is then carried out. It is shown that balancing is generally possible even when the dimensional parameters are imposed, which is a useful property since dimensional parameters are usually obtained from kinematic design or optimization. Finally, examples of balanced planar and spatial parallel manipulators are given. Static balancing leads to considerable reduction in the actuator forces (or torques), which in turn leads to less powerful actuators and more efficient designs. Moreover, the possibility of balancing existing systems by introducing additional elements, as demonstrated here, is of interest for retrofitting existing parallel mechanisms.

Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1463-1477 ◽  
Author(s):  
Houssem Saafi ◽  
Houssein Lamine
Keyword(s):  
Design Optimization ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Analysis And Design ◽  
Planar Parallel Manipulator ◽  
Forward Kinematic ◽  
Planar Parallel Manipulators

SUMMARYThis paper investigates a comparative kinematic analysis between nonredundant and redundant 2-Degree Of Freedom parallel manipulators. The nonredundant manipulator is based on the Five-Bar mechanism, and the redundant one is a 3-RRR planar parallel manipulator. This study is aimed to select the best structure for a haptic application. This latter requires a mechanism with a desired workspace of 10 cm × 10 cm and an admissible force of 5 N in all directions. The analysis criteria are the accuracy of the forward kinematic model and the required actuator torques. Thereby, the geometric parameters of the two structures are optimized in order to satisfy the required workspace such that parallel singularities are overcome. The analysis showed that the nonredundant optimally designed manipulator is more suitable for the haptic application.

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