An algebraic approach to cooperative rotations in networks of interconnected rigid units

2018 ◽  
Vol 74 (5) ◽  
pp. 408-424 ◽  
Author(s):  
Branton Campbell ◽  
Christopher J. Howard ◽  
Tyler B. Averett ◽  
Thomas A. Whittle ◽  
Siegbert Schmid ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Algebraic Approach ◽  
Functional Materials ◽  
Linear System Of Equations ◽  
Rotational Degrees Of Freedom ◽  
Rigid Unit Modes ◽  
Symmetry Mode ◽  
Entire Network

Crystalline solids consisting of three-dimensional networks of interconnected rigid units are ubiquitous amongst functional materials. In many cases, application-critical properties are sensitive to rigid-unit rotations at low temperature, high pressure or specific stoichiometry. The shared atoms that connect rigid units impose severe constraints on any rotational degrees of freedom, which must then be cooperative throughout the entire network. Successful efforts to identify cooperative-rotational rigid-unit modes (RUMs) in crystals have employed split-atom harmonic potentials, exhaustive testing of the rotational symmetry modes allowed by group representation theory, and even simple geometric considerations. This article presents a purely algebraic approach to RUM identification wherein the conditions of connectedness are used to construct a linear system of equations in the rotational symmetry-mode amplitudes.

scholarly journals A comparison of three-dimensional rotation formalisms for least-squares and Bayesian inverse kinematics

2021 ◽  
Author(s):  
Ben Serrien ◽  
Klevis Aliaj ◽  
Todd Pataky
Keyword(s):  
Least Squares ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Estimation Error ◽  
Computational Cost ◽  
Three Dimensional ◽  
Linear Least Squares ◽  
Computationally Efficient ◽  
Rotational Degrees Of Freedom ◽  
Value Decomposition

Marker-based inverse kinematics (IK) is prone to errors arising from measurementnoise and soft-tissue artefacts. Various least-squares and Bayesian methods canbe applied to limit the estimation error to a minimum. Recently proposed meth-ods like Bayesian IK come at an increased computational cost however. In thistechnical paper, we present an overview of eight different least squares or BayesianIK methods, including their accuracy and computational load for IK problemsinvolving a single rigid body and three rotational degrees-of-freedom, whose at-titude is estimated from four noisy marker positions. The results indicate thatNon-Linear Least Squares, Variational Bayesian and full Bayesian IK are supe-rior to Singular Value Decomposition in terms of accuracy, with approximatelya two-fold error reduction. However, only Non-Linear Least Squares and Varia-tional Bayesian IK are computationally efficient enough to scale towards practicaluse in biomechanical applications, with computational durations of 1-10 ms; fullyBayesian procedures required approximately 30 s for single rotation calculations.All Python code and supplementary material can be found in this paper’s GitHubrepository: https://github.com/benserrien/pybik.

A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

2019 ◽  
Vol 11 (1) ◽  
pp. 67-78
Author(s):  
Kamel Meftah ◽  
Lakhdar Sedira
Keyword(s):  
Finite Element ◽  
Strain Field ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Field Tensor ◽  
Tetrahedral Element ◽  
Numerical Studies ◽  
Rotational Degrees Of Freedom ◽  
Tensor Approximation

Abstract The paper presents a four-node tetrahedral solid finite element SFR4 with rotational degrees of freedom (DOFs) based on the Space Fiber Rotation (SFR) concept for modeling three-dimensional solid structures. This SFR concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. Full numerical integration is used to evaluate the element stiffness matrix. To demonstrate the efficiency and accuracy of the developed four-node tetrahedron solid element and to compare its performance with the classical four-node tetrahedral element, extensive numerical studies are presented.

Novel Design and Three-Dimensional Printing of Variable Stiffness Robotic Grippers

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Yang Yang ◽  
Yonghua Chen ◽  
Ying Wei ◽  
Yingtian Li
Keyword(s):  
3D Printing ◽  
Degrees Of Freedom ◽  
Shape Memory Polymer ◽  
Three Dimensional ◽  
Acrylonitrile Butadiene Styrene ◽  
Variable Stiffness ◽  
Analytical Models ◽  
Printing Process ◽  
Finger Joints ◽  
Rotational Degrees Of Freedom

In this paper, a novel robotic gripper design with variable stiffness is proposed and fabricated using a modified additive manufacturing (hereafter called 3D printing) process. The gripper is composed of two identical robotic fingers and each finger has three rotational degrees-of-freedom as inspired by human fingers. The finger design is composed of two materials: acrylonitrile butadiene styrene (ABS) for the bone segments and shape-memory polymer (SMP) for the finger joints. When the SMP joints are exposed to thermal energy and heated to above their glass transition temperature (Tg), the finger joints exhibit very small stiffness, thus allow easy bending by an external force. When there is no bending force, the finger will restore to its original shape thanks to SMP's shape recovering stress. The finger design is actuated by a pneumatics soft actuator. Fabrication of the proposed robotic finger is made possible by a modified 3D printing process. An analytical model is developed to represent the relationship between the soft actuator's air pressure and the finger's deflection angle. Furthermore, analytical modeling of the finger stiffness modulation is presented. Several experiments are conducted to validate the analytical models.

scholarly journals A new meta-module design for efficient reconfiguration of modular robots

2021 ◽  
Author(s):  
Irene Parada ◽  
Vera Sacristán ◽  
Rodrigo I. Silveira
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Central Point ◽  
The Other ◽  
Three Dimensions ◽  
Modular Robots ◽  
The Novel ◽  
Modular Robot ◽  
Module Design ◽  
Rotational Degrees Of Freedom

AbstractWe propose a new meta-module design for two important classes of modular robots. The new meta-modules are three-dimensional, robust and compact, improving on the previously proposed ones. One of them applies to so-called edge-hinged modular robot units, such as M-TRAN, SuperBot, SMORES, UBot, PolyBot and CKBot, while the other one applies to so-called central-point-hinged modular robot units, which include Molecubes and Roombots. The new meta-modules use the rotational degrees of freedom of these two types of robot units in order to expand and contract, as to double or halve their length in each of the two directions of its three dimensions, therefore simulating the capabilities of Crystalline and Telecube robots. Furthermore, in the edge-hinged case we prove that the novel meta-module can also perform the scrunch, relax and transfer moves that are necessary in any tunneling-based reconfiguration algorithm for expanding/contracting modular robots such as Crystalline and Telecube. This implies that the use of meta-meta-modules is unnecessary, and that currently existing efficient reconfiguration algorithms can be applied to a much larger set of modular robots than initially intended. We also prove that the size of the new meta-modules is optimal and cannot be further reduced.

scholarly journals The ISOTILT software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Branton J. Campbell ◽  
Harold T. Stokes ◽  
Tyler B. Averett ◽  
Shae Machlus ◽  
Christopher J. Yost
Keyword(s):  
Null Space ◽  
Software Tool ◽  
Software Suite ◽  
Web Based ◽  
Linear System Of Equations ◽  
Displacement Vectors ◽  
Rigid Unit Modes ◽  
Value Decomposition ◽  
User Friendly ◽  
Symmetry Mode

A user-friendly web-based software tool called `ISOTILT' is introduced for detecting cooperative rigid-unit modes (RUMs) in networks of interconnected rigid units (e.g. molecules, clusters or polyhedral units). This tool implements a recently described algorithm in which symmetry-mode patterns of pivot-atom rotation and displacement vectors are used to construct a linear system of equations whose null space consists entirely of RUMs. The symmetry modes are first separated into independent symmetry-mode blocks and the set of equations for each block is solved separately by singular value decomposition. ISOTILT is the newest member of the ISOTROPY Software Suite. Here, it is shown how to prepare structural and symmetry-mode information for use in ISOTILT, how to use each of ISOTILT's input fields and options, and how to use and interpret ISOTILT output.

scholarly journals Effects of Prosthetic Socket Design on Residual Femur Motion Using Dynamic Stereo X-Ray - A Preliminary Analysis

2021 ◽  
Vol 9 ◽  
Author(s):  
Jason T. Maikos ◽  
John M. Chomack ◽  
J. Peter Loan ◽  
Kathryn M. Bradley ◽  
Susan E. D’Andrea
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Residual Limb ◽  
Transfemoral Amputation ◽  
X Ray ◽  
Prosthetic Socket ◽  
Rotational Degrees Of Freedom ◽  
Socket Technology ◽  
Effectiveness Studies ◽  
Analytical Tools

Individuals with transfemoral amputation experience relative motion between their residual limb and prosthetic socket, which can cause inefficient dynamic load transmission and secondary comorbidities that limit mobility. Accurately measuring the relative position and orientation of the residual limb relative to the prosthetic socket during dynamic activities can provide great insight into the complex mechanics of the socket/limb interface. Five participants with transfemoral amputation were recruited for this study. All participants had a well-fitting, ischial containment socket and were also fit with a compression/release stabilization socket. Participants underwent an 8-wk, randomized crossover trial to compare differences between socket types. Dynamic stereo x-ray was used to quantify three-dimensional residual bone kinematics relative to the prosthetic socket during treadmill walking at self-selected speed. Comfort, satisfaction, and utility were also assessed. There were no significant differences in relative femur kinematics between socket types in the three rotational degrees of freedom, as well as anterior-posterior and medial-lateral translation (p > 0.05). The ischial containment socket demonstrated significantly less proximal-distal translation (pistoning) of the femur compared to the compression/release stabilization socket during the gait cycle (p < 0.05), suggesting that the compression/release stabilization socket provided less control of the residual femur during distal translation. No significant differences in comfort and utility were found between socket types (p > 0.05). The quantitative, dynamic analytical tools used in the study were sensitive to distinguish differences in three-dimensional residual femur motion between two socket types, which can serve as a platform for future comparative effectiveness studies of socket technology.

Delayed Position-Feedback Controller for the Reduction of Payload Pendulations of Rotary Cranes

2003 ◽  
Vol 9 (1-2) ◽  
pp. 257-277 ◽  
Author(s):  
Ziyad N. Masoud ◽  
Ali H. Nayfeh ◽  
Amjed Al-Mousa
Keyword(s):  
Control Strategy ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Scaled Model ◽  
Heavy Equipment ◽  
Position Feedback ◽  
Out Of Plane ◽  
Rotary Crane ◽  
Rotational Degrees Of Freedom ◽  
Successful Control

In this paper, we show that, in rotary cranes, it is possible to reduce payload pendulations significantly by controlling the crane's translational and rotational degrees of freedom. Such a control can be achieved with the heavy equipment that is already part of the crane, so that retrofitting existing cranes with such a controller would require little effort. Moreover, the control is superimposed transparently on the commands of the operator. The successful control strategy is based on delayed position feedback of the payload's in-plane and out-of-plane motions. Its effectiveness is demonstrated with a fully nonlinear three-dimensional computer simulation and with an experiment on a scaled model of a rotary crane. The results demonstrate that the pendulations can be significantly reduced, and therefore the rate of operation can be greatly increased. The effectiveness of the controller is demonstrated for both rotary and gantry modes of operation.

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