Parallel mechanisms with dependent motions of the moving platform

2011 ◽  
pp. 553-599
Author(s):  
Grigore Gogu
Keyword(s):  
Parallel Mechanisms ◽  
Moving Platform

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

WRENCH-CLOSURE WORKSPACE OF SIX-DOF PARALLEL MECHANISMS DRIVEN BY 7 CABLES

2005 ◽  
Vol 29 (4) ◽  
pp. 541-552 ◽  
Author(s):  
Marc Gouttefarde ◽  
Clément M. Gosselin
Keyword(s):  
Cross Sections ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Six Dof ◽  
Moving Platform ◽  
Six Degree Of Freedom

The wrench-closure workspace (WCW) of six-degree-of-freedom (DOF) parallel cable-driven mechanisms is defined as the set of poses of the moving platform of the mechanism for which any external wrench can be balanced by tension forces in the cables. This workspace is fundamental in order to analyze and design parallel cable-driven mechanisms. This paper deals with the class of six-DOF mechanisms driven by seven cables. Two theorems, which provide efficient means to test whether a given pose of the moving platform belongs to the WCW, are proposed. One of these two theorems reveals the nature of the boundary of the constant-orientation cross sections of the WCW. Moreover, some of the possible applications of these theorems are discussed and illustrated.

scholarly journals Reconfiguration Analysis of a 3-DOF Parallel Mechanism

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
The Third ◽  
Equilateral Triangles ◽  
Moving Platform

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

A class of reconfigurable parallel mechanisms with five-bar metamorphic linkage

2016 ◽  
Vol 231 (11) ◽  
pp. 2089-2099 ◽  
Author(s):  
Chunxu Tian ◽  
Yuefa Fang ◽  
Sheng Guo ◽  
Haibo Qu
Keyword(s):  
Potential Application ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Constraint Force ◽  
Motion Modes ◽  
Moving Platform ◽  
Five Phases ◽  
Serial Chains

This paper presents a planar five-bar metamorphic linkage which has five phases resulting from locking of motors. Reconfigurable limbs are constructed by integrating the five-bar metamorphic linage as sub-chains. The branch transition of metamorphic linkage is analyzed. By adding appropriate joints to the planer five-bar metamorphic linkage, reconfigurable limbs whose constraint can switch among no constraint, a constrained force and a constrained couple are obtained. Serial limb structures that can provide a constraint force and a constraint couple are synthesized based on screw theory. Reconfigurable limbs that have five configurations associated with the five phases of the five-bar metamorphic linkage are assembled with 4-DOF (degrees-of-freedom) serial chains. A class of reconfigurable parallel mechanisms is derived by connecting the moving platform to the base with three identical kinematic limbs. These parallel mechanisms can perform various output motion modes such as 3T, 3R, 2T1R, 1T2R, 3T1R, 2T2R, 1T3R, 2T3R, 3T2R and 3T3R. Finally, the potential application of the proposed mechanisms is analyzed and conclusions are drawn.

Parallel mechanisms with decoupled rotation of the moving platform in planar motion

2009 ◽  
Vol 224 (3) ◽  
pp. 709-720 ◽  
Author(s):  
G Gogu
Keyword(s):  
Translational Motion ◽  
Planar Motion ◽  
Parallel Mechanisms ◽  
Structural Synthesis ◽  
Linear Transformations ◽  
New Family ◽  
Current Article ◽  
Moving Platform ◽  
First Time

The current article presents a new family of T2R1-type spatial parallel mechanisms (PMs) with decoupled and unlimited rotation of the moving platform in planar motion. The moving platform performs two independent translations (T2) and one independent unlimited rotation (R1) whose axis is perpendicular to the plane of translations. A method is proposed for structural synthesis of T2R1-type PMs based on the theory of linear transformations. The moving platform has unlimited rotational capabilities and is decoupled with respect to translational motion. To the best of the author's knowledge, this article presents for the first time solutions of T2R1-type spatial PMs with decoupled and unlimited rotation of the moving platform in planar motion.

Axodes Analysis of the Multi DOF Parallel Mechanisms and Parasitic Motion

2013 ◽  
Author(s):  
Ziming Chen ◽  
Huafeng Ding ◽  
Wenao Cao ◽  
Zhen Huang
Keyword(s):  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Screw Axis ◽  
Spatial Mechanism ◽  
Parasitic Motion ◽  
Screw Motions ◽  
Instantaneous Screw Axis ◽  
Moving Platform ◽  
Instantaneous Screw ◽  
General Motion

The general motion of a spatial mechanism is a screw motion about an instantaneous screw axis (ISA). The locus of a series of ISAs will form a ruled surface, which can be called as an axode. For a spatial mechanism with only one degree of freedom (DOF), the ISAs or the axodes of the moving platform are unique. However, the axodes of the parallel mechanisms (PMs) with multi DOF are related to the specific motion which has various possibilities. In this paper, the ISAs of the multi DOF PMs are studied using the jacobian matrix which is changing with the configurations of the moving platform. The axodes of the multi DOF PMs with different inputs or outputs are obtained using this method. Based on the analyzed results, it is very clear that the general motions of the PMs are screw motions or rotations about a series of ISAs. In the end, the parasitic motion of the PMs is studied. For a PM, the parasitic motion will exist if the rotational freedoms are not rotations about a fixed point or axis.

Dynamic Balancing of Multi-Degree-of-Freedom Parallel Mechanisms With Multiple Legs

2004 ◽  
Author(s):  
Yangnian Wu ◽  
Cle´ment M. Gosselin
Keyword(s):  
Numerical Simulations ◽  
Degree Of Freedom ◽  
Effective Algorithm ◽  
Parallel Mechanisms ◽  
Dynamic Balancing ◽  
Dynamic Equivalence ◽  
Moving Platforms ◽  
Moving Platform

This paper systematically presents an effective algorithm for the dynamic balancing of multi-degree-of-freedom parallel mechanisms with multiple legs and the dynamic equivalence between point masses and arbitrary moving platforms. The mass and inertia of the moving platform are replaced by point masses located at the points of attachment of the legs to the platform and the mechanisms are balanced by considering each of the legs independently. The validity and feasibility of this algorithm is first verified both theoretically and using numerical simulations in ADAMS. Two, three and four point masses are respectively discussed for different cases. Finally, some reactionless planar and spatial multi-degree-of-freedom parallel mechanisms synthesized based on this algorithm are given.

A Family of Novel Lower-Mobility Decoupled Parallel Mechanisms

2007 ◽  
Author(s):  
Daxing Zeng ◽  
Sijun Zhu ◽  
Zhen Huang
Keyword(s):  
Real Time ◽  
Basic Feature ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Real Time Control ◽  
Motion Feature ◽  
Time Control ◽  
Fixed Base ◽  
Lower Mobility ◽  
Moving Platform

This paper presents a family of novel lower-mobility decoupled parallel mechanisms (DPMs), which consists of one 5-DOF (degree of freedom) DPM, two 4-DOF DPMs, three 3-DOF DPMs, and three 2-DOF DPMs. The basic feature of this family is that the moving platform and the fixed base of the DPMs are connected by two limbs and the motion of the moving platform is fully decoupled. Then the constraint screw method is used to analyze the motion feature of all DPMs presented in this paper. The mobility of these DPMs has also been calculated by the Modified Grubler-Kutzbach criterion. All the DPMs in this paper are simple and no computation is required for real-time control.

Force Analysis of Spatial Single Closed-Loop Overconstrained Mechanisms

2016 ◽  
Author(s):  
Wenlan Liu ◽  
Yundou Xu ◽  
Jiantao Yao ◽  
Yongsheng Zhao
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Driving Forces ◽  
Parallel Mechanisms ◽  
Force Analysis ◽  
Moving Platform ◽  
Compliance Matrices ◽  
Overconstrained Mechanisms ◽  
Force Problem ◽  
Deformation Compatibility

Taking the Bennett and Schatz mechanisms as examples, force analyses of spatial single closed-loop (SSCL) overconstrained mechanisms are demonstrated aiming to obtain the driving forces/torques and joint reactions of this kind of mechanisms. Firstly, regarding the SSCL overconstrained mechanisms as parallel mechanisms with two supporting limbs, the constraint wrenches and actuation wrenches imposed on the moving platform by the two limbs are discussed, and the mobility of each mechanism is analyzed based on the screw theory. Then, the compliance matrices of the limbs’ constraint wrenches are derived, which contribute to solve the statically indeterminate force problem of the mechanisms. Next, by combining the force and moment equilibrium equation of the moving platform with the deformation compatibility equation of the corresponding mechanism, the magnitudes of all constraint wrenches and actuation wrenches are solved. Furthermore, the driving forces/torques and joint reactions are derived. Finally, the numerical and simulation results of the two mechanisms are presented.

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