The Realization of Desired Stiffness of Parallel Mechanism by Adding Redundantly-Actuated Limbs

2017 ◽  
Author(s):  
Shunzhou Huang ◽  
Jue Yu ◽  
Hao Wang ◽  
Yong Zhao ◽  
Xinmin Lai
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulators ◽  
Stewart Platform ◽  
Industrial Applications ◽  
Parallel Mechanisms ◽  
Normal Stiffness ◽  
Stiffness Properties ◽  
Mirror Milling ◽  
Redundantly Actuated ◽  
Mapping Models

Stiffness performance is of importance for the use of parallel manipulators in the industrial applications. For this consideration, this paper proposes to realize the desired stiffness properties of parallel mechanism by adding redundantly-actuated limbs. Based on the stiffness mapping models of both the full-DOF and limited-DOF parallel mechanisms, the stiffness variation rules when redundant limbs is introduced into the mechanism are discussed. Moreover, an algorithm for designing the types and configurations of redundant limbs is studied. Two cases are investigated to validate the presented approach. One is about the stiffness decoupling of the Stewart platform, the other is focused on the enhancement of normal stiffness of a Tricept supporting mechanism used in a mirror milling machine designed by us. The result shows that the stiffness performance of Stewart platform can be decoupled when adding six redundantly-actuated limbs that are symmetric with the original active limbs. Besides, the normal stiffness of Tricept mechanism can be enhanced significantly by transforming the passive UP chain to be a redundant actuated chain.

Workspace Analysis of a Novel Six-Degrees-of-Freedom Parallel Manipulator With Coaxial Actuated Arms

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Mats Isaksson ◽  
Matthew Watson
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Limited Range ◽  
Parallel Mechanisms ◽  
Six Degrees Of Freedom ◽  
Serial Robots ◽  
High Acceleration ◽  
Redundantly Actuated

Parallel manipulators possess several advantages compared to serial robots, including the possibilities for high acceleration and high accuracy positioning of the manipulated platform. However, the majority of all proposed parallel mechanisms suffer from the combined drawbacks of a small positional workspace in relation to the manipulator footprint and a limited range of rotations of the manipulated platform. This paper analyses a recently proposed six-degrees-of-freedom parallel mechanism that aims to address both these issues while maintaining the traditional advantages of a parallel mechanism. The investigated manipulator consists of six actuated coaxial upper arms that are allowed to rotate indefinitely around a central cylindrical base column and a manipulated platform where five of the six joint positions are collinear. The axis-symmetric arm system leads to an extensive positional workspace while the proposed link arrangement increases the range of achievable platform rotations. The manipulator workspace is analyzed in detail and two methods to further increase the rotational workspace are presented. It is shown that the proposed manipulator has the possibility of a nonsingular transition of assembly modes, which extends the usable workspace. Furthermore, it is demonstrated how an additional kinematic chain can be utilized to achieve infinite platform rotation around one platform axis. By introducing additional mobility in the manipulated platform, a redundantly actuated mechanism is avoided.

scholarly journals Calibration Method for a Parallel Mechanism Type Machine Tool by Response Surface Methodology –Consideration via Simulation on a Stewart Platform Mechanism–

2010 ◽  
Vol 4 (4) ◽  
pp. 355-363 ◽  
Author(s):  
Hiroshi Yachi ◽  
◽  
Hiroshi Tachiya
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Parallel Mechanism ◽  
Measurement Data ◽  
Calibration Method ◽  
Stewart Platform ◽  
Parallel Mechanisms ◽  
Data Set ◽  
Efficient Data ◽  
Efficient Measurement

This paper proposes a calibration method for parallel mechanisms usingResponse Surface Methodology. This method is a statistical approach to estimating an unknown input-output relationship using a small set of efficient data collected on an intended system. Although identifying locations causing positional errors in a parallel mechanism and precisely measuring the position and posture of the output point are difficult, the proposed calibration method based onResponse Surface Methodologyaims to compensate for positional and postural errors, without indentifying the locations causing these errors, by using a small yet efficient measurement data set. This study analyzes the effectiveness of the method we propose by applying it to a Stewart platform, which is a typical spatial 6-DOF parallel mechanism.

A Comparison of Architectures of Parallel Mechanisms for Workspace and Kinematic Properties

1995 ◽  
Author(s):  
Clement M. Gosselin ◽  
Rémi Ricard ◽  
Meyer A. Nahon
Keyword(s):  
Parallel Manipulators ◽  
Parallel Architectures ◽  
Parallel Mechanisms ◽  
Design And Optimization ◽  
Stiffness Properties ◽  
Structural Differences ◽  
Six Degree Of Freedom ◽  
Kinematic Properties ◽  
Better Than ◽  
Normalization Factors

Abstract This paper presents a study of the workspace and kinematic properties of four different architectures of six-degree-of-freedom parallel mechanisms. For each architecture, the volume of the Cartesian workspace is computed at different orientations of the moving platform. The distribution of the workspace is also found by computing the 2D sections of the 3D workspace. The rotational workspace is then determined at the reference position of the platform. Finally, the stiffness properties of the architectures are obtained. Normalization factors are then defined to account for the structural differences between the architectures of mechanisms. The comparison of the different architectures of parallel mechanisms has been performed using SIMPA, a specialized CAD tool developed for the kinematic analysis and optimization of parallel manipulators. The results thus obtained illustrate the range of performance which can be expected from different parallel architectures. Although none of the architectures proves to be better than all the others in all respects, particular architectures do excel in particular performance measures. The approach proposed would therefore be useful in further studies relating to the design and optimization of parallel manipulators and mechanisms.

Kinematic Calibration for Redundantly Actuated Parallel Mechanisms

2004 ◽  
Vol 126 (2) ◽  
pp. 307-318 ◽  
Author(s):  
Jay il Jeong ◽  
Dongsoo Kang ◽  
Young Man Cho ◽  
Jongwon Kim
Keyword(s):  
Optimization Algorithm ◽  
Parallel Mechanism ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Geometrical Constraint ◽  
Kinematic Parameters ◽  
Angle Error ◽  
Calibration Algorithm ◽  
Redundantly Actuated

We present a new kinematic calibration algorithm for redundantly actuated parallel mechanisms, and illustrate the algorithm with a case study of a planar seven-element 2-degree-of-freedom (DOF) mechanism with three actuators. To calibrate a nonredundantly actuated parallel mechanism, one can find actual kinematic parameters by means of geometrical constraint of the mechanism’s kinematic structure and measurement values. However, the calibration algorithm for a nonredundant 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 (meaning position and orientation). 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-DOF parallel mechanism 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.

scholarly journals Collision-free workspace of parallel mechanisms based on an interval analysis approach

Robotica ◽  
2016 ◽  
Vol 35 (8) ◽  
pp. 1747-1760 ◽  
Author(s):  
MohammadHadi FarzanehKaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro
Keyword(s):  
Interval Analysis ◽  
Parallel Mechanism ◽  
Spherical Shape ◽  
Stewart Platform ◽  
Analysis Approach ◽  
Parallel Mechanisms ◽  
Planar Case ◽  
End Effector ◽  
Mechanical Interference

SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

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.

Optimal trajectory planning considering optimal torque distribution of redundantly actuated parallel mechanism

2018 ◽  
Vol 232 (23) ◽  
pp. 4410-4419 ◽  
Author(s):  
Sumin Park ◽  
Jongwon Kim ◽  
Giuk Lee
Keyword(s):  
Parallel Mechanism ◽  
Optimization Procedure ◽  
Optimal Operation ◽  
Operation Planning ◽  
Parallel Mechanisms ◽  
Planning Stage ◽  
End Effector ◽  
Torque Distribution ◽  
Redundantly Actuated ◽  
Two Stages

Previous studies on the optimal operation planning of redundantly actuated parallel mechanisms have focused on optimal torque distribution for a predefined trajectory. However, the optimized result obtained for a predefined trajectory cannot guarantee an optimal operation plan, because the torque distribution ability of a redundantly actuated parallel mechanism is highly dependent on the shape of the end-effector trajectory. Therefore, we can expect the redundantly actuated parallel mechanism performance to be enhanced when both the trajectory and torque distribution are optimized during the optimal operation planning stage. We propose a novel redundantly actuated parallel mechanism optimization procedure that can optimize both the end-effector trajectory and torque distribution. The proposed procedure is composed of two stages of optimizers, i.e. upper- and lower-level optimizers that generate the end-effector trajectory and distribute the torques along the generated trajectory, respectively. Composition of these two stages of the optimization procedure allows optimization of both the trajectory and torque distribution, despite the correlation between them. The proposed optimization procedure is simulated using two types of cost functions. All the simulation results show that the proposed procedure facilitates optimization of the end-effector trajectory and the torque distribution concurrently. Also, the cost function value is minimized to a greater extent than in the result with the optimal torque distribution along the initial trajectory.

Projection-Based Control of Parallel Mechanisms

2011 ◽  
Vol 6 (3) ◽  
Author(s):  
Farhad Aghili
Keyword(s):  
Mechanical System ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Actuator Saturation ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Dynamics Model ◽  
Minimal Order ◽  
Control Approach ◽  
System Changes

The unifying idea for most model-based control approaches for parallel mechanism is to derive a minimal-order dynamics model of the system and then design the corresponding controller. The problem with such a control approach is that the controller needs to change its structure whenever the mechanical system changes its number of degrees-of-freedom. This paper presents a projection-based control scheme for parallel mechanism that works whether the system is overactuated or not; it does not require derivation of the minimal-order dynamics model. Since the dimension of the projection matrix is fixed, the projection-based controller does not need to change its structure whenever the mechanical system changes its number of degrees-of-freedom. The controller also allows to specify lower and upper bounds on the actuator forces/torques, making it suitable not only for the control of parallel manipulators with limited force/torque capability of the actuators but also for backlash-free control of parallel manipulators as well as for control of tendon driven parallel manipulators. The stability of the projection-based controllers is rigourously proved, while the condition for the controllability of parallel manipulators is also derived in detail. Finally, experimental results obtained from a simple parallel mechanism, which changes its degrees-of-freedom, are appended. The results also demonstrate that the maximum actuator torque can be reduced by 20% if the actuator saturation is taken into account by the controller.

Closed-Form Direct Position Analysis of a 5–5 Parallel Mechanism

1993 ◽  
Vol 115 (3) ◽  
pp. 515-521 ◽  
Author(s):  
C. Innocenti ◽  
V. Parenti-Castelli
Keyword(s):  
Closed Form ◽  
Parallel Mechanism ◽  
General Feature ◽  
Polynomial Equation ◽  
Stewart Platform ◽  
Parallel Mechanisms ◽  
Complex Field ◽  
Output Link ◽  
Degree Polynomial ◽  
Displacement Analysis

The paper presents the closed form direct displacement analysis for a class of Stewart platform-type parallel mechanisms whose general feature consists of six legs which meet five distinct points both in the base and in the movable output link. Out of the two possible arrangements, only one is here analyzed in detail. Given a set of actuator displacements the analysis provides all the possible locations of the platform relative to the base. The analysis results in a 40th degree polynomial equation in one unknown. The roots of the equation provide in the complex field forty closures of the mechanism. This new result has been numerically verified by the inverse displacement analysis.

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.

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