scholarly journals The Kinematic Sensitivity of Robotic Manipulators to Joint Clearances

2010 ◽  
Author(s):  
Nicolas Binaud ◽  
Philippe Cardou ◽  
Ste´phane Caro ◽  
Philippe Wenger
Keyword(s):  
Reference Point ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Error Prediction ◽  
Orientation Error ◽  
Moving Platform ◽  
Joint Clearances ◽  
Kinematic Sensitivity ◽  
Quadratically Constrained ◽  
Clearance Model

The paper deals with the kinematic sensitivity of robotic manipulators to joint clearances. First, an error prediction model applicable to both serial and parallel manipulators is developed. A clearance model associated with axisymmetrical joints, which are widely used in robotic manipulators, is also proposed. Then, two nonconvex quadratically constrained quadratic programs (QCQPs) are formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. Finally, the contributions of the paper are highlighted by means of two illustrative examples.

Rotatability of the Floating Link on Multi-Loop Planar Linkages

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Rotation Angle ◽  
Parallel Manipulators ◽  
Orientation Error ◽  
Joint Rotation ◽  
Position Uncertainty ◽  
End Effector ◽  
Uncertainty Model ◽  
Branch Formation ◽  
Joint Clearances ◽  
Planar Linkages

Abstract This paper proposes a method to deal with the orientation uncertainty problem affected by joint clearances. To solve this problem, it is necessary to establish the theory of mobility of the floating link of multi-loop linkages. Since the theory of the mobility of floating link is yet complete, this paper provides a simple treatment to determine the rotatability between any two links, adjoined or not, in planar multi-loop linkages. The rotation angle of the floating link with respect to the reference link is defined so that there is no ambiguity in analyzing the rotation range of the floating link. Based on the joint rotation space (JRS) method, one may identify not only the branch formation but also the rotatability between any two links on each of the branches. It is a visualized method that reveals the rotation characteristic of multi-loop linkages. This paper demonstrates the rotation range of the floating link with respect to the reference link on six-bar Stephenson linkages, 2-degree-of-freedom (DOF). 7-bar linkages, and 3-DOF. Eight-bar parallel manipulators. This might be the first paper to deal with the rotatability of 3-DOF planar multi-loop linkages. This paper uses the method to predict the clearance-induced angle uncertainty of the 8-bar parallel manipulators, which determines the worst orientation error of the end-effector and fills up the void of the joint clearance uncertainty model proposed by Ting et al. (2017, “Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators,” J. Mech. Rob., 9, p. 061001).

scholarly journals Sensitivity Analysis of 3-RPR Planar Parallel Manipulators

2009 ◽  
Vol 131 (12) ◽  
Author(s):  
Stéphane Caro ◽  
Nicolas Binaud ◽  
Philippe Wenger
Keyword(s):  
Sensitivity Analysis ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Sensitivity Coefficients ◽  
Sensitivity Indices ◽  
Moving Platform ◽  
Planar Parallel Manipulators

This paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators (PPMs). First, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Moreover, two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, a methodology is proposed to compare 3-RPR PPMs with regard to their dexterity, workspace size and sensitivity. Finally, the sensitivity of a 3-RPR PPM is analyzed in detail and four 3-RPR PPMs are compared as illustrative examples.

A new class of isotropic generators for developing 6-DOF isotropic manipulators

Robotica ◽  
2008 ◽  
Vol 26 (5) ◽  
pp. 619-625 ◽  
Author(s):  
K. Y. Tsai ◽  
T. K. Lee ◽  
Y. S. Jang
Keyword(s):  
Reference Point ◽  
Parallel Manipulators ◽  
Geometric Constraint ◽  
Kinematic Chains ◽  
New Class ◽  
New Methods ◽  
Center Point ◽  
Different Types ◽  
Different Shapes ◽  
Straight Lines

SUMMARYDeveloping 6-DOF isotropic manipulators using isotropic generators is simple and efficient, and isotropic generators can be employed to develop serial, redundant, or parallel isotropic manipulators. An isotropic generator consists of a reference point and six straight lines. The existing generators, however, have one common geometric constraint: the reference point is equidistant from the six straight lines. Some practical isotropic designs might not be obtained due to this constraint. This paper proposes methods for developing new isotropic generators. The generators thus developed are not subject to the constraint, and the new methods allow us to specify the location of the tool center point, the size of the platform or the base, or the shape of isotropic parallel manipulators. Many new generators are presented to develop 6-DOF parallel manipulators with different shapes or different types of kinematic chains.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators

2017 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu
Keyword(s):  
Kinematic Model ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Position Uncertainty ◽  
Joint Clearances ◽  
Planar Linkages ◽  
Oscillation Characteristics ◽  
Linkage Model ◽  
Input Error

The paper presents a simple and effective kinematic model and methodology, based on Ting’s N-bar rotatability laws [2629], to assess the extent of the position uncertainty caused by joint clearances for any linkage and manipulators connected with revolute or prismatic pairs. The model is derived and explained with geometric rigor based on Ting’s rotatability laws. The significant contribution includes (1) the clearance link model for P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearance from the input error, (2) a simple uncertainty linkage model that features a deterministic instantaneous structure mounted on non-deterministic flexible legs, (3) the generality of the method, which is effective for multiloop linkages and parallel manipulators. The discussion is carried out through symmetrically constructed planar eight-bar parallel robots. It is found that the uncertainty region of a three-leg parallel robot is enclosed by a hexagon, while that of its serial counterpart is enclosed by a circle inscribed by the hexagon. A numerical example is also presented. The finding and proof, though only based on three-leg planar 8-bar parallel robots, may have a wider implication suggesting that based on kinematics, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in parallel robots cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

Stiffness Analysis of a Spatial Parallel Mechanism With Flexible Moving Platform

2010 ◽  
Author(s):  
Amir Rezaei ◽  
Alireza Akbarzadeh ◽  
Javad Enferadi
Keyword(s):  
Inverse Kinematics ◽  
Strain Energy ◽  
Parallel Manipulators ◽  
Physical Structure ◽  
Fem Model ◽  
Lumped Model ◽  
Stiffness Analysis ◽  
Spatial Parallel Mechanism ◽  
Inverse Kinematics Problem ◽  
Moving Platform

In this paper, stiffness analysis of a 3-DOF spatial, 3-PSP type, parallel manipulator is investigated. Most previous stiffness analysis studies of parallel manipulators are performed using lumped model as well as assuming a rigid moving platform. In this paper, unlike traditional stiffness analysis, the moving platform is assumed to be flexible. Additionally, a continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano’s theorem [1]. For this purpose, first we solve inverse kinematics problem then We must find relationship between the applied external torques on the moving platform and the resultant joints forces. Next, strain energy moving platform is calculated. Strain energy of this element is calculated using force analysis and inverse kinematics problem. Finally, a FEM model is generated and used to simulate the physical structure. Simulation results are compared with the analytical model.

Analysis of Varying Natural Frequencies and Damping Ratios of a Sample Parallel Manipulator Throughout its Workspace Using Linearized Equations of Motion

2001 ◽  
Author(s):  
Kris Kozak ◽  
Imme Ebert-Uphoff ◽  
William Singhose
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Parallel Architecture ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Dynamic Equations ◽  
Extreme Variation

Abstract This article investigates the dynamic properties of robotic manipulators of parallel architecture. In particular, the dependency of the dynamic equations on the manipulator’s configuration within the workspace is analyzed. The proposed approach is to linearize the dynamic equations locally throughout the workspace and to plot the corresponding natural frequencies and damping ratios. While the results are only applicable for small velocities of the manipulator, they present a first step towards the classification of the nonlinear dynamics of parallel manipulators. The method is applied to a sample manipulator with two degrees-of-freedom. The corresponding numerical results demonstrate the extreme variation of its natural frequencies and damping ratios throughout the workspace.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

Type Synthesis of Variable Degrees-of-Freedom Parallel Manipulators With Both Planar and 3T1R Operation Modes

2012 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Operation Modes ◽  
Moving Platform ◽  
Multiple Operation ◽  
Schönflies Motion

Parallel manipulators (PMs) with multiple operation modes are novel reconfigurable PMs which use less number of actuators and can be reconfigured without disassembly. Although several classes of PMs with multiple operation modes that have the same DOF (degrees-of-freedom) in all the operation modes have been proposed, only one class of variable-DOF PMs with multiple operation modes — PMs with multiple operation modes that do not have the same DOF in all the operation modes — have been proposed so far. This paper deals with the type synthesis of variable-DOF PMs with both planar and 3T1R (or Schönflies motion which has three translational DOF and 1 rotational DOF) operation modes. The axes of rotation of the moving platform in the planar operation mode are not parallel to the axes of rotation of the moving platform in the 3T1R operation mode. At first, an approach to the type synthesis of PMs with multiple operation modes is recalled. Based on the results on the type synthesis of planar PMs and 3T1R PMs, the types of variable-DOF PMs with both planar and 3T1R operation modes are then obtained. This work can be extended to the type synthesis of other classes of PMs with multiple operation modes.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

Sign in / Sign up

Export Citation Format

Share Document