A General Formula of Degree-of-Freedom for Parallel Manipulators and Its Application

2006 ◽  
Author(s):  
Ting-Li Yang ◽  
Dong-Jin Sun
Keyword(s):  
Characteristic Equation ◽  
Topological Structure ◽  
Topological Analysis ◽  
Parallel Manipulators ◽  
Characteristic Matrix ◽  
Parallel Mechanisms ◽  
Constraint Equations ◽  
Analysis And Synthesis ◽  
Dimension Type ◽  
Symbolic Operation

This paper presents a new DOF formula for mechanism Its main feature is that the calculation of mobility has a single value for a given mechanism without the set of constraint equations, each of parameters in the formula can be correctly determined by simple symbol operation. The formula shows the map relationship between DOF and topological structure of a mechanism. It is embodied in the following aspects: (1) Dimension type: so that topological structure of a mechanism can be represented by symbols. (2) Orientation and location characteristic matrix: so that rank of a mechanism can be calculated by symbolic operation. (3) Orientation and location characteristic equation of serial mechanism and its symbolic operation. (4) Orientation and location characteristic equation of parallel mechanism and its symbolic operation. (5) The DOF calculation based on orientation and location characteristic equations of serial and parallel mechanisms. The DOF formula presented in this paper has already been used for topological analysis and synthesis of parallel mechanisms and its advantages has been proven.

Position and Orientation Characteristic Equation for Topological Design of Serial Mechanisms

2008 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Peng Shen ◽  
...  
Keyword(s):  
Topological Structure ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Geometrical Meaning ◽  
Topological Design ◽  
Operation Rules ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
Position And Orientation ◽  
Symbolic Operation

This paper presents the explicit mapping relations between topological structure of mechanism and position and orientation characteristic (abbreviated as POC hereafter) of its motion output link. It deals with: (1) The symbolic representation and the invariant of topological structure of mechanism; (2) The matrix representation of POC of mechanism motion output; (3) The POC equation of serial mechanism and its symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules, and has clear geometrical meaning. So it is easy to use. The POC equation can be used for structural analysis and synthesis of serial and parallel mechanisms. The method proposed in this paper is totally different from the methods based on screw theory and based on displacement subgroup/sub-manifold.

REPRESENTATIONS AND IDENTIFICATIONS OF STRUCTURAL AND MOTION STATE CHARACTERISTICS OF MECHANISMS WITH VARIABLE TOPOLOGIES

2006 ◽  
Vol 30 (1) ◽  
pp. 19-40 ◽  
Author(s):  
Hong-Sen Yan ◽  
Chin-Hsing Kuo
Keyword(s):  
Topological Structure ◽  
Topological Analysis ◽  
State Machines ◽  
Matrix Representations ◽  
Motion State ◽  
New Concepts ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Finite State ◽  
State Graphs

A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). This paper is developed for the structural and motion state representations and identifications of MVTs. For representing the topological structures of MVTs, a set of methods including graph and matrix representations is proposed. For representing the motion state characteristics of MVTs, the idea of finite-state machines is employed via the state tables and state graphs. And, two new concepts, the topological homomorphism and motion homomorphism, are proposed for the identifications of structural and motion state characteristics of MVTs. The results of this work provide a logical foundation for the topological analysis and synthesis of mechanisms with variable topologies.

Position and Orientation Characteristic Equation for Topological Design of Parallel Mechanisms

2008 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Topological Structure ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Output Link ◽  
Geometrical Meaning ◽  
Operation Rules ◽  
The Matrix ◽  
Position And Orientation ◽  
Symbolic Operation

This paper presents the explicit mapping relations between topological structure of parallel mechanism and position and orientation characteristic (in short, POC) of its motion output link. It deals with: (1) The symbolic representation and the invariant of topological structure of mechanism; (2) The matrix representation of POC of motion output link; (3) The POC equations of parallel mechanism and its symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules, and has clear geometrical meaning. So, it is easy to use. The forward operation of the POC equations can be used for structural analysis; its inverse operation can be used for structural synthesis. The method proposed in this paper is totally different from the methods based on screw theory and based on displacement subgroup.

Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Topological Structure ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Structural Synthesis ◽  
Geometrical Meaning ◽  
Single Loop ◽  
Operation Rules ◽  
The Matrix ◽  
Position And Orientation ◽  
Symbolic Operation

This paper presents the explicit mapping relations between topological structure and position and orientation characteristic (POC) of mechanism motion output. It deals with (1) the symbolic representation and the invariant property of the topological structure of the mechanism, (2) the matrix representation of POC of mechanism motion output, and (3) the POC equations of serial and parallel mechanisms and the corresponding symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules and has clear geometrical meaning, so it is easy to use. The POC equations cannot only be used for structural analysis of the mechanism (such as determining POC of the relative motion between any two links of a mechanism and the rank of single-loop kinematic chain and calculating the full-cycle DOF of a mechanism, etc.) but can be used for structural synthesis of the mechanism as well (e.g., structural synthesis of the rank-degenerated serial mechanism, the over constrained single-loop mechanism, and the rank-degenerated parallel mechanism, etc.).

Non-overconstrained 3-dof spherical parallel manipulators of type: 3-RCC, 3-CCR, 3-CRC

Robotica ◽  
2005 ◽  
Vol 24 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Mourad Karouia ◽  
Jacques M. Hervé
Keyword(s):  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Structural Type ◽  
Parallel Mechanisms ◽  
Structural Types ◽  
Special Cases ◽  
Algebraic Properties ◽  
Analysis And Synthesis ◽  
Fixed Base ◽  
Type 3

Non-overconstrained 3-dof spherical parallel manipulators of a structural type 3-RCC, 3-CCR, 3-CRC are introduced. The mechanism has three limbs that connect in parallel the moving platform to the fixed base. Each limb is an opened kinematic chain made of a sequence of one revolute pair R and two cylindrical pairs C. The orientation of the end-effector is obtained by actuating simultaneously the three limbs. A structural type analysis and synthesis, which is based on the algebraic properties of a Lie group of the displacement set, is employed to find the geometrical conditions for the assembly of these spherical parallel mechanisms and also the structurally singular configurations. Then an enumeration of the structural types is given and remarkable special cases of orientational mechanisms are also described, namely 3-HGR, 3-RGH and 3-HGH.

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.

scholarly journals Introduction to the special issue: parallel manipulators.

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 353-353
Author(s):  
François Pierrot
Keyword(s):  
North America ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Special Issue ◽  
Industrial Areas

It has been a pleasure for me to arrange this Special Issue of Robotica on Parallel Robots which provides 9 papers from authors from Asia, Oceania, North America and Europe; worldwide research on this topic is proof of the growing interest of both the scientific and the industrial areas of parallel mechanisms. I truly believe that the main reason for this enthusiasm is that parallel mechanisms research extends from theoretical mathematics and kinematics to applied robotics, and even beyond, creating new technological challenges.

A Statically Balanced Gough/Stewart-Type Platform: Conception, Design, and Simulation

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Marco Carricato ◽  
Clément Gosselin
Keyword(s):  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Theoretical Point ◽  
Constant Force ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Neutral Equilibrium ◽  
The Difference ◽  
Elastic Elements

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical designs of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in equilibrium in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. The performance of a study prototype is simulated via a model in both static and dynamic conditions, in order to prove the feasibility of the proposed design. The effects of imperfect balancing, due to the difference between the payload inertial characteristics and the theoretical/nominal ones, are investigated. Under a theoretical point of view, formal and novel derivations are provided of the necessary and sufficient conditions allowing (i) a body arbitrarily rotating in space to rest in neutral equilibrium under the action of general constant-force generators, (ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy, and (iii) a leg of a Gough/Stewart-type manipulator to operate as a constant-force generator.

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