Type synthesis of spatial 3-DoF parallel mechanisms with planar sub-chains using revised digital topological graphs and arrays

Robotica ◽  
2015 ◽  
Vol 35 (2) ◽  
pp. 370-383 ◽  
Author(s):  
Yi Lu ◽  
Nijia Ye ◽  
Ling Ding
Keyword(s):  
Closed Loop ◽  
Degree Of Freedom ◽  
Digital Topology ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Simple Derivation ◽  
Topological Graphs ◽  
Topology Graph

SUMMARYType synthesis of spatial 3-DoF (degree of freedom) parallel mechanisms (PMs) with planar sub-chains is studied using the revised digital topology graph (r-DTGs) and arrays. First, many DTGs for type synthesis of spatial 3-DoF PMs are derived from their contracted graphs (CGs). Second, a complicated derivation of the DTG and an identification of an isomorphic DTG are transformed into a simple derivation of an array and an identification of an isomorphic array using a compiled program. Third, one or more spatial closed-loop chains in the derived DTGs are changed into the planar closed-loop chains by modifying digits marked in closed-loop chains, and the DTGs are transformed into the r-DTGs for the type synthesis of the spatial 3-DoF PMs with planar sub-chains. Finally, the 52 novel spatial 3-DoF PMs with the planar sub-chains are synthesized and verified by simulation mechanisms.

Type synthesis of four-degree-of-freedom parallel mechanisms using valid arrays and topological graphs with digits

2014 ◽  
Vol 228 (16) ◽  
pp. 3039-3053 ◽  
Author(s):  
Yi Lu ◽  
Ying Wang ◽  
Ling Ding
Keyword(s):  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Simple Derivation ◽  
Topological Graphs ◽  
Synthesis Approach

The type synthesis of four-degree-of-freedom parallel mechanisms using valid arrays and the valid topology graphs with digits is studied. First, the 12 contracted graphs without any binary links for type synthesis of the four-degree-of-freedom parallel mechanisms are constructed. Second, a complicated derivation of topology graphs with digit is transformed into a simple derivation of array, many valid arrays are derived, and many invalid arrays and invalid topology graphs with digit are determined and removed from the arrays using a compiled program. Third, many valid topology graphs with digit with various basic links are derived from the valid arrays, and the 46 different four-degree-of-freedom parallel mechanisms are synthesized using the valid topology graphs with digit and arrays, in which eight existing four-degree-of-freedom parallel mechanisms are included. Finally, the degree of freedoms of synthesized parallel mechanisms are calculated to verify the correction and effectiveness of type synthesis approach using valid arrays and the valid topology graphs with digit.

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.

scholarly journals Type Synthesis of 5-DoF Parallel Mechanisms with Different Submechanisms

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yi Lu ◽  
Yang Lu ◽  
Lijie Zhang ◽  
Nijia Ye ◽  
Bo Hu ◽  
...  
Keyword(s):  
Degree Of Freedom ◽  
Digital Topology ◽  
Parallel Mechanisms ◽  
Type Synthesis

The type synthesis of the 5-DoF (degree of freedom) parallel mechanisms with different submechanisms is studied by utilizing digital topology graphs (DTGs). The conditions for synthesizing the 5-DoF parallel mechanisms with different submechanisms using DTGs are determined. Many valid DTGs are derived from 17 different 5-DoF associated linkages, and the valid DTGs are transformed into revised DTGs. The subplanar and/or spatial parallel mechanisms in the 5-DoF parallel mechanisms are transformed into some simple equivalent limbs, and their equivalent relations and merits are analyzed. Using the derived valid DTGs and revised DTGs, many 5-DoF parallel mechanisms with different subserial or parallel mechanisms are synthesized, and they are simplified by replacing the complicated subparallel mechanisms with their simple equivalent limbs. Finally, their DoFs are calculated to verify the correctness and effectiveness of the proposed approach.

Autoderivation of Topological Graphs for Type Synthesis of Planar 3DOF Parallel Mechanisms

2009 ◽  
Vol 2 (1) ◽  
Author(s):  
Yi Lu ◽  
Ling Ding ◽  
Jianping Yu
Keyword(s):  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Topological Graph ◽  
Topological Graphs

The autoderivation of valid topological graph (TGs) of planar 3DOF parallel mechanisms is studied systematically based on topology embryonic graphs (TEGs) and arrays. First, some TEGs without any binary links are constructed, some paths with only binary links are distributed over the TEGs, and some valid TGs of the planar 3DOF PMs are derived. Second, a complicated derivation of the TG is transformed into an easy derivation of array. Third, some programs are compiled in VB, all valid arrays corresponding to nonisomorphic TGs are derived automatically, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined by compiled programs. Finally, many valid TGs of planar 3DOF PMs with various basic links are derived from valid arrays.

Singularity Analysis of 5-RPRRR Parallel Mechanisms via Grassmann Line Geometry

2009 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Cle´ment Gosselin
Keyword(s):  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Line Geometry ◽  
Singular Configurations ◽  
Highly Nonlinear ◽  
Grassmann Line Geometry

This paper investigates the singular configurations of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical legs of the RPUR type. The general mechanism was recently revealed by performing the type synthesis for symmetrical 5-DOF parallel mechanisms. In this study, some simplified designs are proposed for which the singular configurations can be predicted by means of the so-called Grassmann line geometry. This technique can be regarded as a powerful tool for analyzing the degeneration of the Plu¨cker screw set. The main focus of this contribution is to predict the actuation singularity, for a general and simplified design, without expanding the determinant of the inverse Jacobian matrix (actuated constraints system) which is highly nonlinear and difficult to analyze.

Type Synthesis of Three-Degree-of-Freedom Translational Compliant Parallel Mechanisms

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Cong Yue ◽  
Ying Zhang ◽  
Hai-Jun Su ◽  
Xianwen Kong
Keyword(s):  
Screw Theory ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Design Stage ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Geometric Conditions ◽  
Synthesis Procedure ◽  
Flexure Joints ◽  
Three Degree Of Freedom

In this paper, we apply screw theory to type synthesis of compliant parallel mechanisms (PMs) with translational degree-of-freedom (DOF). Compliant PMs are formed by a moving platform supported by three or more limbs each of which is a serial chain of flexure joints and rigid bodies. They achieve movement through the deformation of flexure joints and have been widely used in precision machinery. As an important task in the conceptual design stage, the goal of type synthesis is to determine the chain of each limb as well as their relationship when they are assembled in parallel for a prescribed motion pattern. In our approach, we study a category of commonly used flexure primitives and flexure elements whose freedom and constraint spaces are characterized by twists and wrenches in screw theory. Following the well-studied synthesis procedure for rigid body PMs, we propose a synthesis procedure for compliant PMs via screw theory. As an example, we demonstrate the procedure for synthesizing compliant PMs with three translational DOF. Tables of limbs, types, and geometric conditions for the assemblies of these limbs are presented. The paper provides a catalog of 3DOF translational compliant PM designs. At last, we developed finite element simulation to validate one of the synthesized designs.

Type Synthesis of 3-DOF Rotational Parallel Mechanisms With No Intersecting Axes

2012 ◽  
Author(s):  
Ziming Chen ◽  
Wen-ao Cao ◽  
Zhen Huang
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Constraint Force ◽  
New Approach ◽  
Spherical Parallel Mechanism ◽  
Rotational Motions

Parallel mechanisms which can realize three rotational motions are very important in the parallel mechanism family. Not the same with the traditional spherical parallel mechanism, a new kind of 3-DOF (degree of freedom) rotational parallel mechanism with no intersecting axes (RPMNIA) are proposed in this paper. This kind of rotational parallel mechanisms have the advantages of easy manufacturing. A new approach using the screw theory and the subchain theory is proposed to design the branches with only one constraint force and some new one-force-branches are found. Using these new branches, a group of 3-DOF rotational parallel mechanisms without intersecting axes are synthesized.

Parallel robots with configurable platforms: Fundamental aspects of a new class of robotic architectures

2015 ◽  
Vol 230 (3) ◽  
pp. 463-472 ◽  
Author(s):  
Patrice Lambert ◽  
Just L Herder
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Dynamic Performance ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
New Class ◽  
Contact Points ◽  
The Subject ◽  
High Dynamic

This paper introduces general and fundamental aspects of a new class of parallel robots termed “parallel robots with configurable platforms”. The concept behind parallel mechanisms with configurable platforms is that the rigid link (non-configurable) end-effector is replaced by an additional closed-loop chain (the configurable platform). Some of the links of this closed loop are attached to the limbs so both the position and the configuration of the platform can be fully controlled from the motors located on the base. They retain the advantages of classical parallel robots, i.e. that all the motors are grounded on the base, while offering mechanical grasping capabilities via multiple contact points. Despite the few studies that have been done yet on the subject, the possible range of applications for this type of architecture is promising since it would be suitable for any application requiring both controlled grasping capabilities and high dynamic performance. This paper provides some preliminary results regarding the topology, mobility, overconstraints, Jacobian matrix, singularities and type synthesis of parallel robots with configurable platforms.

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