Screw theory-based stiffness analysis for a fluidic-driven soft robotic manipulator

This paper aims to investigate how to determine the basic parameters of the helical compression spring which supports a symmetrical cable-driven hybrid joint (CDHJ) towards the elbow joint of wheelchair-mounted robotic manipulator. The joint design of wheelchair-mounted robotic manipulator needs to consider lightweight but robust, workspace requirements, and variable stiffness elements, so we propose a CDHJ which becomes a variable stiffness joint due the spring under bending and compression provides nonlinear stiffness characteristics. Intuitively, different springs will make the workspace and stiffness of CDHJ different, so we focus on studying the spring effects on workspace and stiffness of CDHJ for its preliminary design. The key to workspace and stiffness analysis of CDHJ is the cable tension, the key to calculate the cable tension is the lateral bending and compression spring model. The spring model is based on Castigliano’s theorem to obtain the relationship between spring force and displacement. The simulation results verify the correctness of the proposed spring model, and show that the spring, with properly chosen parameters, can increase the workspace of CDHJ whose stiffness also can be adjusted to meet the specified design requirements. Then, the modelling method can be extended to other cable-driven mechanism with a flexible compression spring.

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Stiffness Modeling of the Soft-Finger Contact in Robotic Grasping

Journal of Mechanical Design ◽

10.1115/1.1758255 ◽

2004 ◽

Vol 126 (4) ◽

pp. 646-656 ◽

Cited By ~ 30

Author(s):

Abdul Ghafoor ◽

Jian S. Dai ◽

Joseph Duffy

Keyword(s):

Stiffness Matrix ◽

Screw Theory ◽

Contact Stiffness ◽

Point Contact ◽

Elastic Model ◽

Point Contacts ◽

Stiffness Analysis ◽

Stiffness Properties ◽

Congruence Transformation ◽

Soft Finger

This paper investigates the soft-finger contact by presenting the contact with a set of line springs based on screw theory, reveals the rotational effects, and identifies the stiffness properties of the contact. An elastic model of a soft-finger contact is proposed and a generalized contact stiffness matrix is developed by applying the congruence transformation and by introducing stiffness mapping of the line springs in translational directions and rotational axes. The effective stiffnesses along these directions and axes are hence obtained and the rotational stiffnesses are revealed. This helps create a screw representation of a six-dimensional soft-finger contact and produce an approach of analyzing and synthesizing a robotic grasp without resorting to the point contact representation. The correlation between the rotational stiffness, the number of equivalent point contacts and the number of equivalent contours is given and the stiffness synthesis is presented with both modular and direct approaches. The grasp thus achieved from the stiffness analysis contributes to both translational and rotational restraint and the stiffness matrix so developed is proven to be symmetric and positive definite. Case studies are presented with a two-soft-finger grasp and a three-soft-finger grasp. The grasps are analyzed with a general stiffness matrix which is used to control the fine displacements of a grasped object by changing the preload on the contact.

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Screw theory on spatial stiffness analysis of robots with elastic joints and links

Chinese Journal of Mechanical Engineering ◽

10.3901/cjme.2004.supp.248 ◽

2004 ◽

Vol 17 (supp) ◽

pp. 248 ◽

Cited By ~ 1

Author(s):

Xilun Ding

Keyword(s):

Screw Theory ◽

Stiffness Analysis ◽

Elastic Joints

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Jacobian-based stiffness analysis method for parallel manipulators with non-redundant legs

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215602283 ◽

2015 ◽

Vol 230 (3) ◽

pp. 341-352 ◽

Cited By ~ 14

Author(s):

Antonius GL Hoevenaars ◽

Patrice Lambert ◽

Just L Herder

Keyword(s):

Parallel Manipulator ◽

Screw Theory ◽

Parallel Manipulators ◽

Structural Elements ◽

Analysis Method ◽

End Effector ◽

Stiffness Analysis ◽

Compliant Joints ◽

Lower Mobility ◽

Actuated Joints

Stiffness is an important element in the model of a parallel manipulator. A complete stiffness analysis includes the contributions of joints as well as structural elements. Parallel manipulators potentially include both actuated joints, passive compliant joints, and zero stiffness joints, while a leg may impose constraints on the end-effector in the case of lower mobility parallel manipulators. Additionally, parallel manipulators are often designed to interact with an environment, which means that an external wrench may be applied to the end-effector. This paper presents a Jacobian-based stiffness analysis method, based on screw theory, that effectively considers all above aspects and which also applies to parallel manipulators with non-redundant legs.

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Stiffness Analysis for a Novel Parallel-Robot Based High-Precision Flexible Assembly Fixture

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.364-366.327 ◽

2007 ◽

Vol 364-366 ◽

pp. 327-332 ◽

Cited By ~ 1

Author(s):

Hong Jian Yu ◽

Bing Li ◽

Xiao Jun Yang ◽

Ying Hu ◽

Hong Hu

Keyword(s):

Stiffness Matrix ◽

Screw Theory ◽

System Modeling ◽

Parallel Robot ◽

Parallel Robots ◽

Stiffness Analysis ◽

Flexible Assembly ◽

Global Stiffness Matrix ◽

The Relationship ◽

Assembly Fixture

In this paper, a novel parallel mechanism (3-RRRS/UPR) used in flexible fixture with configuration composed of two parallel robots (2-RR and 3-RRRS/ UPR) is presented. First, system modeling including the mobility study is conducted. Then a novel methodology is proposed that makes use of screw theory to analyze the deformation and stiffness of the mechanism: firstly we identified the existence of the deformation of the subchain, in terms of the relationship between the effective screw and deformation screw; then we took the deformation as an infinitesimal motion of the mechanism, and the stiffness matrix corresponding to the deformation can be deduced. Finally the global stiffness matrix of the whole mechanism is modeled by assembling different stiffness characters based on the presented methodology.

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Stiffness Estimation and Experiments for the Exechon Parallel Self-Reconfiguring Fixture Mechanism

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-70993 ◽

2012 ◽

Cited By ~ 3

Author(s):

Xiong Li ◽

Dimiter Zlatanov ◽

Matteo Zoppi ◽

Rezia Molfino

Keyword(s):

Screw Theory ◽

Virtual Work ◽

Element Analysis ◽

Stiffness Analysis ◽

Stiffness Modeling ◽

Successful Series ◽

Stiffness Model ◽

Stiffness Map ◽

Fixture System ◽

Typical Configuration

The Exechon X150, a new smaller member of a successful series of parallel kinematic machines, has been recently developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. This paper is the first to address the stiffness analysis of the parallel mechanism on which the design is based. The stiffness modeling method uses reciprocal screw theory as well as the virtual work principle, resulting in a simpler formulation and more convenient than ones obtained with traditional stiffness-modeling methods. Based on this model, the stiffness map within the workspace is obtained. The stiffness of the mechanism at a typical configuration is carried out. The complete finite element analysis and simulation used to verify the effectiveness of the stiffness model. Using geometric spatial decomposition, numerical examples of the mechanism at three typical configurations are presented.

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Elastostatic Stiffness Analysis for the US/UPS Parallel Manipulators

Mathematical Problems in Engineering ◽

10.1155/2020/1975428 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Weizhong Zhang ◽

Wei Ye ◽

Chao Yang

Keyword(s):

Strain Energy ◽

Screw Theory ◽

Virtual Work ◽

Element Model ◽

Parallel Manipulators ◽

Modeling Method ◽

Stiffness Analysis ◽

Design And Optimization ◽

Stiffness Matrices ◽

The Us

The virtual joint method (VJM) cannot calculate the strain energy stored in each rod. In order to solve the problem, a modeling method of the elastostatic stiffness was investigated for the UP/UPS parallel manipulators (PMs), taking the example of the 6-SPS PM. The modeling method was based on screw theory, Castigliano’s theorem, and strain energy (where U, P, and S, respectively, denote universal, prismatic, and spherical joints). First, the actuator and constraint wrenches of the mechanism were obtained by screw theory. Second, compact limb stiffness matrices were obtained in terms of strain energy and Castigliano’s second theorem. Finally, analytic expressions for the overall stiffness matrix of the mechanism and the amplitudes of the actuator force were obtained by adopting the virtual work principle and the balance equation for the mobile platform. All relative errors between the results of the analytical model and the finite element model are below 2%, which validates the effectiveness of the elastostatic stiffness model. The virtual work index was adopted to evaluate the stiffness performance of the mechanism, and the results show that the stiffness is not only related to position and orientation but also closely related to the directions of external loads. It is also demonstrated that the method has general adaptability for the stiffness analysis for the US/UPS PMs, laying the foundation for further reasonable dynamic design and optimization of such manipulators.

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