scholarly journals Stiffness Modeling of Robotic-Manipulators Under Auxiliary Loadings

2012 ◽  
Author(s):  
Alexandr Klimchik ◽  
Anatol Pashkevich ◽  
Stéphane Caro ◽  
Damien Chablat
Keyword(s):  
Robotic Manipulators ◽  
Computationally Efficient ◽  
End Effector ◽  
Efficient Procedure ◽  
Stiffness Modeling ◽  
Cartesian Stiffness Matrix ◽  
Different Types ◽  
Mapping Equation ◽  
Linear Force ◽  
Cartesian Stiffness

The paper focuses on the extension of the virtual-joint-based stiffness modeling technique for the case of different types of loadings applied both to the robot end-effector and to manipulator intermediate points (auxiliary loading). It is assumed that the manipulator can be presented as a set of compliant links separated by passive or active joints. It proposes a computationally efficient procedure that is able to obtain a non-linear force-deflection relation taking into account the internal and external loadings. It also produces the Cartesian stiffness matrix. This allows to extend the classical stiffness mapping equation for the case of manipulators with auxiliary loading. The results are illustrated by numerical examples.

Stiffness analysis and comparison of a Biglide parallel grinder with alternative spatial modular parallelograms

Robotica ◽  
2016 ◽  
Vol 35 (6) ◽  
pp. 1310-1326 ◽  
Author(s):  
Guanglei Wu ◽  
Ping Zou
Keyword(s):  
Eigenvalue Problem ◽  
Stiffness Matrix ◽  
Rotational Stiffness ◽  
Stiffness Analysis ◽  
Stiffness Modeling ◽  
Cartesian Stiffness Matrix ◽  
Modeling Analysis ◽  
Cartesian Stiffness

SUMMARYThis paper deals with the stiffness modeling, analysis and comparison of a Biglide parallel grinder with two alternative modular parallelograms. It turns out that the Cartesian stiffness matrix of the manipulator has the property that it can be decoupled into two homogeneous matrices, corresponding to the translational and rotational aspects, through which the principal stiffnesses and the associated directions are identified by means of the eigenvalue problem, allowing the evaluation of the translational and rotational stiffness of the manipulator either at a given pose or the overall workspace. The stiffness comparison of the two alternative Biglide machines reveals the (dis)advantages of the two different spatial modular parallelograms.

New repetitive motion planning scheme with cube end-effector planning precision for redundant robotic manipulators

Robotica ◽  
2021 ◽  
pp. 1-22
Author(s):  
Limin Shen ◽  
Yuanmei Wen
Keyword(s):  
Theoretical Analysis ◽  
Motion Planning ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Repetitive Motion ◽  
End Effector ◽  
Difference Formula ◽  
Planning Scheme ◽  
Simulation Results ◽  
The Difference

Abstract Repetitive motion planning (RMP) is important in operating redundant robotic manipulators. In this paper, a new RMP scheme that is based on the pseudoinverse formulation is proposed for redundant robotic manipulators. Such a scheme is derived from the discretization of an existing RMP scheme by utilizing the difference formula. Then, theoretical analysis and results are presented to show the characteristic of the proposed RMP scheme. That is, this scheme possesses the characteristic of cube pattern in the end-effector planning precision. The proposed RMP scheme is further extended and studied for redundant robotic manipulators under joint constraint. Based on a four-link robotic manipulator, simulation results substantiate the effectiveness and superiority of the proposed RMP scheme and its extended one.

Control of Elastic Systems via Passivity-Based Methods

2004 ◽  
Vol 10 (11) ◽  
pp. 1699-1735 ◽  
Author(s):  
A. G. Kelkar ◽  
S. M. Joshi
Keyword(s):  
Flexible Structures ◽  
Robotic Manipulators ◽  
Mathematical Concept ◽  
Controller Synthesis ◽  
Control Laws ◽  
Linear Elastic ◽  
Elastic Systems ◽  
Different Types ◽  
Linear Controllers ◽  
Synthesis Approach

In this paper we present a controller synthesis approach for elastic systems based on the mathematical concept of passivity. For nonlinear and linear elastic systems that are inherently passive, robust control laws are presented that guarantee stability. Examples of such systems include flexible structures with col-located and compatible actuators and sensors, and multibody space-based robotic manipulators. For linear elastic systems that are not inherently passive, methods are presented for rendering them passive by compensation. The “passified” systems can then be robustly controlled by a class of passive linear controllers that guarantee stability despite uncertainties and inaccuracies in the mathematical models. The controller synthesis approach is demonstrated by application to five different types of elastic systems.

An Approach for the Dynamics of Robotic Manipulators With Structural Flexibility of Links and Joints

1997 ◽  
Author(s):  
J. Kövecses ◽  
R. G. Fenton ◽  
W. L. Cleghorn
Keyword(s):  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Structural Flexibility ◽  
Flexible Link ◽  
Dynamic Effects ◽  
Flexible Joint ◽  
Modeling And Analysis ◽  
Discrete Parameter ◽  
Rigid Link ◽  
Different Types

Abstract In this paper, an approach is presented for the dynamic modeling and analysis of robotic manipulators having structural flexibility in the links and joints. The formulation allows the user to include different types of flexibilities, as required. This approach includes the dynamic effects of joint driving systems by considering the mass and moments of inertia of their elements, the rotor-link interactions, and the gear reduction ratios; all of which can have significant influences on the behavior of the manipulator. Both distributed-discrete and discretized-discrete parameter models of a robot can be analysed. In the discretized-discrete case, dynamic equations of motion are developed for four model types: rigid link - rigid joint, rigid link - flexible joint, flexible link - rigid joint, and flexible link - flexible joint. An example of a two-link manipulator is considered. Simulation results are presented for different models (flexible joint - rigid link, rigid joint - flexible link, flexible joint - flexible link) of the manipulator. The computations show the influence of joint and link flexibilities on the manipulator performance.

Shape Optimum Design of Robotic Manipulators With Static Performance Criteria

1987 ◽  
Author(s):  
D. A. Saravanos ◽  
J. S. Lamancusa ◽  
H. J. Sommer
Keyword(s):  
Finite Element ◽  
Optimum Design ◽  
Robotic Manipulators ◽  
Performance Criterion ◽  
Performance Criteria ◽  
Robotic Arm ◽  
Mass Ratio ◽  
End Effector ◽  
Vibrational Response ◽  
Static Performance

Abstract The end effector deflections of robotic manipulators may be minimized by optimizing the geometric shape and the dimensions of their links. A multiple posture static performance criterion for the prediction of the shape optimum design is presented. An efficient optimization algorithm is developed for the solution of the problem using finite element modeling to predict the compliance of the robotic arm. The method is applied to an existing robotic arm, and the results demonstrate that simple alterations to the dimensions and the shape of the links can greatly improve, not only the stiffness, but also the stiffness/mass ratio and consequently the vibrational response of the manipulator structure.

scholarly journals Rotation-joint stiffness modeling for industrial robots considering contacts

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879306 ◽  
Author(s):  
Zhifeng Liu ◽  
Jingjing Xu ◽  
Qiang Cheng ◽  
Yongsheng Zhao ◽  
Yanhu Pei
Keyword(s):  
Fractal Theory ◽  
Joint Stiffness ◽  
Industrial Robots ◽  
Torsional Stiffness ◽  
Equivalent Stiffness ◽  
Force Analysis ◽  
Joint System ◽  
End Effector ◽  
Stiffness Modeling ◽  
High Speeds

Joint flexibility has a major impact on the motion accuracy of a robotic end effector, particularly at high speeds. This work proposes a technique of precisely modeling the torsional stiffness of the rotational joints for the industrial robots. This technique considers the contacts that exist in the joint system, which can have a significant effect on the overall joint stiffness. The torsional stiffness of the connections that commonly exist in the rotational joints, such as the belt connection, the connections using key, bolts, and pins, were modeled by combining the force analysis and the fractal theory. Through modeling the equivalent stiffness for the springs in serial and in parallel, the torsional stiffness of all joints for the ER3A-C60 robot were calculated and analyzed. The results show that the estimated stiffness based on the proposed technique is closer to the actual values than that based on the previous model without considering the contacts. The analysis is useful for controlling the dynamic characteristic of the industrial robots with the rotational joints while planning the trajectory for the end effector.

Inverse Kinematics of Discretely-Actuated Manipulators Within a Bounded Grid Element

2006 ◽  
Author(s):  
Deanne C. Kemeny ◽  
Raymond J. Cipra
Keyword(s):  
Inverse Kinematics ◽  
Lower Cost ◽  
Robotic Manipulators ◽  
Forward Kinematics ◽  
End Effector ◽  
Grid Element ◽  
The Third ◽  
Inverse Kinematics Problem

Discretely-actuated manipulators are defined in this paper as serial planar chains of many links and are an alternative to traditional robotic manipulators, where continuously variable actuators are replaced with discrete, or digital actuators. Benefits include reduced weight and complexity, and predictable manipulation at lower cost. Challenges to using digital manipulators are the discrete end-effector positions which make the inverse kinematics problem difficult to solve. Furthermore, for a specific application position in the manipulator workspace, there may not be an actual end-effector position. This research has relaxed the inverse kinematics problem around this challenge making each application position an element of a grid in which the end effector must reach. There may be many possible end-effector positions that would reach the element goal, the solution uses the first one that is found. The inverse kinematics solution assumes the assembly configuration of the digital manipulator is already solved specifically for the application grid. The Jacobian function, normally used to solve joint velocities, can be used to identify the exact shift vectors that are used for the inverse kinematics. Three methods to solve this problem are discussed and the third method was implemented as a four-part solution that is a directed and manipulated search for the inverse kinematics solution where all four solutions may be needed. A discussion of forward kinematics and the Jacobian function in relation to digital manipulators is also presented.

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