Computation of the Maximal Singularity-Free Workspace of the MSSM for a Given Orientation

2007 ◽  
Author(s):  
Qimi Jiang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Case Studies ◽  
Numerical Algorithm ◽  
Parallel Mechanism ◽  
Parallel Robots ◽  
Analytic Method ◽  
Robot Design ◽  
Parallel Mechanisms ◽  
Leg Length ◽  
Maximal Singularity ◽  
The Relationship

The maximal singularity-free workspace of parallel mechanisms is a desirable criterion in robot design. However, for a 6-dof parallel mechanism, it is very difficult to find an analytic method to determine the maximal singularity-free workspace around a prescribed point for a given orientation. Hence, a numerical algorithm is presented in this paper to compute the maximal singularity-free workspace as well as the corresponding leg length ranges of the MSSM Gough-Stewart platform. This algorithm is based on the relationship between the maximal singularity-free workspace and the singularity surface. Case studies with different orientations are performed to demonstrate the presented algorithm. The results obtained can be applied to the geometric design or parameter (leg length) setup of the MSSM parallel robots.

The Maximal Singularity-Free Workspace of the Gough–Stewart Platform for a Given Orientation

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Case Studies ◽  
Parallel Mechanism ◽  
Stewart Platform ◽  
Parallel Robots ◽  
Analytic Method ◽  
Robot Design ◽  
Parallel Mechanisms ◽  
Leg Length ◽  
Maximal Singularity ◽  
The Relationship

The maximal singularity-free workspace of parallel mechanisms is a desirable criterion in robot design. However, for a 6DOF parallel mechanism, it is very difficult to find an analytic method to determine the maximal singularity-free workspace around a prescribed point for a given orientation. Hence, a numerical algorithm is presented in this paper to compute the maximal singularity-free workspace as well as the corresponding leg length ranges of the Gough–Stewart platform. This algorithm is based on the relationship between the maximal singularity-free workspace and the singularity surface. Case studies with different orientations are performed to demonstrate the presented algorithm. The obtained results can be applied to the geometric design or parameter (leg length) setup of this type of parallel robots.

Unilateral Manipulability Quality Indices: Generalized Manipulability Measures for Unilaterally Actuated Robots

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Jonathan Eden ◽  
Darwin Lau ◽  
Ying Tan ◽  
Denny Oetomo
Keyword(s):  
System Dynamics ◽  
Physical Properties ◽  
Case Studies ◽  
Arbitrary Number ◽  
System Analysis ◽  
Parallel Robots ◽  
Quality Indices ◽  
Motion Generation ◽  
Workspace Analysis ◽  
The Relationship

The study of the relationship between the desired system dynamics and the actuation wrench producing those dynamics is important for robotic system analysis. For traditionally actuated robots, the quality indices of dexterity and manipulability quantify this relationship. However, for unilaterally actuated robots (UARs), such as grasping hands and cable-driven parallel robots (CDPRs), these indices cannot be applied due to the unilateral actuation constraint. In this paper, the quality indices of unilateral dexterity (UD) and unilateral maximum force amplification (UMFA) are established for UARs with arbitrary number of actuators. It is shown that these quality indices provide task-independent quantifications of the physical properties of robustness and force amplification for UARs, and they can measure the mechanism’s capability both in singular and nonsingular poses. With these indices, manipulability ellipsoid-derived measures can be applied to arbitrary UARs. The significance of the quality indices for robot synthesis and motion generation analysis is illustrated through two case studies: a five-fingered grasp selection problem and the workspace analysis of a spatial CDPR.

The Manta and the Kanuk: Novel 4-DOF Parallel Mechanisms for Industrial Handling

1999 ◽  
Author(s):  
Luc H. Rolland
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Parallel Robot ◽  
Chain Structure ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Low Mass ◽  
Loading And Unloading ◽  
Very High

Abstract Two novel 4-DOF very fast parallel robots were designed. This paper introduces the new parallel mechanism designs which are named the Manta and the Kanuk. In order to reduce manipulator overall costs, the actuator and encoder numbers are minimized to the exact effective degrees-of-freedoms (DOF) which is usually not the case in most parallel robot designs. The robots allow end-effector displacements along the three Cartesian translations and one platform transversal rotation. The two remaining rotations are blocked by the intrinsic mechanical structure including the rotation along the platform normal which is always limited in range. The main advantages are high stiffness through the multiple kinematic chain structure which allow for low mass designs. Moreover, they feature simple mechanical construction. Thus, it shall be possible to achieve very high throughput since high accelerations are feasible. To circumvent the known workspace limitations, the actuators were selected to be prismatic along linear axes. The applications are automated warehouse manipulation, mediatheque manipulation, machine tool tool changers, loading and unloading.

Investigations on the principle of full decoupling and type synthesis of 2R1T and 2R parallel mechanisms

2019 ◽  
Vol 43 (2) ◽  
pp. 263-271 ◽  
Author(s):  
Yundou Xu ◽  
Bei Wang ◽  
Zhifeng Wang ◽  
Yun Zhao ◽  
Wenlan Liu ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Rotational Degrees Of Freedom ◽  
The Relationship

Based on the relationship between constraint wrenches and rotational axes, the principle of full decoupling of two rotational degrees of freedom (DOFs) for a two-rotation and one-translation (2R1T) parallel mechanism and two-rotation (2R) parallel mechanism with three supporting branches is systematically analyzed. Two conditions for full decoupling of two rotational DOFs of such mechanisms are obtained. The relationship between the two rotational axes of the parallel mechanisms is classified into two cases: intersecting and different. Next, based on the two conditions, type synthesis of the 2R1T and 2R parallel mechanisms with fully decoupled two rotational DOFs is carried out. A series of novel 2R1T and 2R parallel mechanisms with fully decoupled two rotational DOFs are obtained, such as RPU–UPR–RPR. Several of these mechanisms contain only eight single-DOF passive joints, one fewer than in existing mechanisms of this type, and thus have broad applications.

Sliding Mode Set-Point Control of a Three-DOF Cable-Suspended Parallel Robot With Uncertain Mass and Disturbances

2019 ◽  
Author(s):  
Ping Ren ◽  
Xu Sheng
Keyword(s):  
Sliding Mode ◽  
Sufficient Conditions ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Set Point ◽  
Point Motion ◽  
Actuation Scheme ◽  
Three Degree Of Freedom ◽  
The Relationship

Abstract Cable-Suspended Parallel Robots (CSPRs) utilize winches and cables as the actuation scheme instead of rigid links, which renders them advantages of both parallel mechanisms and cable mechanisms. In this paper, a robust sliding mode controller was designed for a three-degree-of-freedom CSPR with uncertain end-effector mass and external disturbances. To control the motions of CSPRs is usually challenging due to the unidirectional constraints of cable tensions. Based on interval analysis, a set of analytical inequalities is obtained which establish the relationship between the cables’ tension constraints and the controller parameters. The sufficient conditions of the controller parameters satisfying the constraints are obtained for the set-point motion subject to uncertainties. Numerical simulations are presented to verify the effectiveness of the proposed approach.

GEOMETRIC OPTIMIZATION OF PLANAR 3-RPR PARALLEL MECHANISMS

2007 ◽  
Vol 31 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Equilateral Triangle ◽  
Unit Area ◽  
Geometric Optimization ◽  
Parallel Mechanisms ◽  
Leg Length ◽  
Simple Singularity ◽  
Maximal Singularity ◽  
Important Concern ◽  
Singularity Locus ◽  
Similar Triangles

To pursue the maximal singularity-free workspace of parallel mechanisms is a very important concern for robot designers. This paper focuses on the case of planar 3-RPR parallel mechanisms. First, a relatively simple singularity equation of any point on the platform is derived. The obtained singularity equation shows that the singularity locus of any point on the platform is a circle of the same size, as long as the base and the platform are similar triangles. Furthermore, the three centres of the workspace circles lie exactly on the singularity circle. With these useful observations, the singularity-free workspace as well as the maximal leg length ranges can be determined. For a base of unit area, it is found that robots with equilateral triangle base and platform can obtain the maximal singularity-free workspace. Three case studies demonstrate this observation. Finally, a procedure for this kind of robot geometric design is provided.

Kinematic Calibration for Redundantly Actuated Parallel Mechanisms: Theory and Application for 2-DOF Mechanism

2004 ◽  
Author(s):  
Jay il Jeong ◽  
Dongsoo Kang ◽  
Jongwon Kim
Keyword(s):  
Optimization Algorithm ◽  
Parallel Mechanism ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Angle Error ◽  
Calibration Algorithm ◽  
Redundantly Actuated ◽  
Relationship Of ◽  
The Relationship

We present a new kinematic calibration algorithm for redundantly actuated parallel mechanisms. The calibration algorithm for a non-redundant case does not apply for a redundantly actuated parallel mechanism, because the angle error of the actuating joint varies with position and the geometrical constraint fails to be consistent. Such change of joint angle error comes from constraint torque variation with each kinematic pose. To calibrate a redundant parallel mechanism, one therefore has to consider constraint torque equilibrium and the relationship of constraint torque to torsional deflection, in addition to geometric constraint. In this paper, we develop the calibration algorithm for a redundantly actuated parallel mechanism using these three relationships, and formulate cost functions for an optimization algorithm. As a case study, we executed the calibration of a 2-degree of freedom (DOF) parallel mechanism with three actuators using the developed algorithm. Coordinate values of tool plate were measured using a laser ball bar and the actual kinematic parameters were identified with a new cost function of the optimization algorithm. Experimental results showed that the accuracy of the tool plate improved by 82% after kinematic calibration in a redundant actuation case.

Dualities in the Analysis of Mechanisms With Multiple Loops and Parallel Mechanisms With Loops in Their Connecting Chains

2004 ◽  
Author(s):  
Koichi Sugimoto
Keyword(s):  
Dynamic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Body System ◽  
Multi Body ◽  
The Relationship

There exists a duality relationship between a twist and a wrench in the dynamics of a mechanism or a multi-body system. Using this relationship, the coordinate-free expressions for the dynamic analysis of multi-loop mechanisms is derived. In the analysis, a Jacobian matrix expressing the relationship among loops is defined, and it is clarified, by using this matrix, that both twists and wrenches can be easily analyzed based on the duality relationship among them. A parallel mechanism having connecting chains with loops is also analyzed, and it is shown that the same procedure can be applied to a parallel mechanism with connecting chains, each loop of which has a motion space that is different from that of the mechanism.

On the Maximization of Joint Velocities and Generalized Reactions in the Workspace and Singularity Analysis of Parallel Mechanisms

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 675-690 ◽  
Author(s):  
Pavel Laryushkin ◽  
Victor Glazunov ◽  
Ksenia Erastova
Keyword(s):  
Case Studies ◽  
External Load ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
State Of The Art ◽  
Singularity Analysis ◽  
The State ◽  
Parallel Mechanisms ◽  
Different Types

SummaryAn approach for calculating the maximum possible absolute values of joint velocities or generalized reactions in a leg of a parallel mechanism has been considered in this paper. The Jacobian analysis and the Screw theory-based methods have been used to acquire the result. These values are calculated for the “worst” directions of the external load or end-effector’s velocity for each leg. The feasibility of using these parameters as the measures of closeness to different types of parallel mechanism singularity is discussed. Further, how this approach is related to the state-of-the-art methods has been illustrated. The key aspect of the discussed approach is that the normalization of vectors or screws is carried out separately for angular and linear components. One possible advantage of such an approach is that it deals only with the kinematic and statics of the mechanism while still providing physically meaningful and practically applicable measures. Case studies of a 3-Degrees Of Freedom translational parallel mechanism and a planar parallel mechanism are presented for illustration and comparison.

Direct Kinematic Analysis of the Spatial Parallel Mechanism with 3-R(P)S Structure Based on the Point Pair Relationship

2021 ◽  
pp. 1-23
Author(s):  
Ganmin Zhu ◽  
Shimin Wei ◽  
Ying Zhang ◽  
Qizheng Liao
Keyword(s):  
Kinematic Analysis ◽  
Geometric Modeling ◽  
Parallel Mechanism ◽  
Computational Method ◽  
Parallel Mechanisms ◽  
Point Pair ◽  
Spatial Parallel Mechanism ◽  
The Family ◽  
Distance Relationship ◽  
The Relationship

Abstract This paper demonstrates a novel geometric modeling and computational method of the family of spatial parallel mechanisms with 3-R(P)S structure for direct kinematic analysis based on the point pair relationship. The point pair relationship, which is derived from the framework of conformal geometric algebra (CGA), consists of the relationship between the point and the point pair and two point pairs. The first research is on the distance relationship between the point and the point pair. Secondly, the derivation of the distance relationship between two point pairs is based on the aforementioned result, which shows the mathematical homogeneity. Thirdly, two formulations for a point of the point pairs that satisfy the distance relationship between two point pairs are reduced. Fourthly, the point pair relationship is applied to solve the direct kinematic analysis of the spatial parallel mechanism with 3-R(P)S structure. Finally, four numerical examples are provided to verify the validity of the proposed algorithm. Overall, the proposed method can be generalized for the direct kinematics of a series of spatial parallel mechanisms with 3-R(P)S structure.

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