Nonholonomic Systems With Redundant Degrees of Freedom Can Exploit Nonlinear Frequency Response to Improve Speed and Efficiency of Locomotion

2020 ◽  
Author(s):  
Vitaliy Fedonyuk ◽  
Colin Rodwell ◽  
Phanindra Tallapragada
Keyword(s):  
Degrees Of Freedom ◽  
Mobile Robotics ◽  
Nonholonomic Constraints ◽  
Nonholonomic Systems ◽  
Torsional Stiffness ◽  
Nonlinear Frequency ◽  
Chaplygin Sleigh ◽  
Additional Degree ◽  
Swimming Motion ◽  
Elastic Potentials

Abstract Rigid body nonholonomic systems serve as models for locomotion of several terrestrial animals such as snakes as well as for fish-like swimming motion. Several well known nonholonomic systems have also found applications in the field of mobile robotics in everything from wheeled vehicles to articulated snake like robots. However, one aspect of their dynamics has remained unexplored. This is to do with the effects of increasing the degrees of freedom by adding additional ‘segments’ such as in a chain, with the joints between segments having a nonzero torsional stiffness. Such nonholonomic systems when subjected to periodic actuation or inputs have additional modes of oscillation. The interplay of the nonholonomic constraints, linear elastic potentials and additional degrees of freedom can produce rich frequency-amplitude response in the dynamics of the system and can lead to significantly higher speed and efficiency. In this paper we explore such dynamics with the example of a well known nonholonomic system, the Chaplygin sleigh and a variant of it with an additional degree of freedom. Such models can be expected to better match the dynamics of biological swimmers and have widespread applications for soft and under-actuated robots.

scholarly journals Annular Defects Impair the Mechanical Stability of the Intervertebral Disc

2021 ◽  
pp. 219256822110060
Author(s):  
Jun-Xin Chen ◽  
Yun-He Li ◽  
Jian Wen ◽  
Zhen Li ◽  
Bin-Sheng Yu ◽  
...  
Keyword(s):  
Intervertebral Disc ◽  
Degrees Of Freedom ◽  
Mechanical Stability ◽  
Biomechanical Testing ◽  
Bending Stiffness ◽  
Biomechanical Study ◽  
Torsional Stiffness ◽  
P Value ◽  
Lateral Bending ◽  
Flexion Extension

Study Design: A biomechanical study. Objectives: The purpose of this study was to investigate the effects of cruciform and square incisions of annulus fibrosus (AF) on the mechanical stability of bovine intervertebral disc (IVD) in multiple degrees of freedom. Methods: Eight bovine caudal IVD motion segments (bone-disc-bone) were obtained from the local abattoir. Cruciform and square incisions were made at the right side of the specimen’s annulus using a surgical scalpel. Biomechanical testing of three-dimensional 6 degrees of freedom was then performed on the bovine caudal motion segments using the mechanical testing and simulation (MTS) machine. Force, displacement, torque and angle were recorded synchronously by the MTS system. P value <.05 was considered statistically significant. Results: Cruciform and square incisions of the AF reduced both axial compressive and torsional stiffness of the IVD and were significantly lower than those of the intact specimens ( P < .01). Left-side axial torsional stiffness of the cruciform incision was significantly higher than a square incision ( P < .01). Neither incision methods impacted flexional-extensional stiffness or lateral-bending stiffness. Conclusions: The cruciform and square incisions of the AF obviously reduced axial compression and axial rotation, but they did not change the flexion-extension and lateral-bending stiffness of the bovine caudal IVD. This mechanical study will be meaningful for the development of new approaches to AF repair and the rehabilitation of the patients after receiving discectomy.

Modeling of nonlinear torsional vibration of the automotive powertrain

2016 ◽  
Vol 24 (9) ◽  
pp. 1774-1786 ◽  
Author(s):  
Sérgio J Idehara ◽  
Fernando L Flach ◽  
Douglas Lemes
Keyword(s):  
Natural Frequency ◽  
Torsional Vibration ◽  
Degrees Of Freedom ◽  
Front Wheel ◽  
Torsional Stiffness ◽  
Bench Test ◽  
Passenger Car ◽  
Engine Torque ◽  
Friction Moment ◽  
Wheel Drive

A vibration model of the powertrain can be used to predict its dynamic behavior when excited by fluctuations in the engine torque and speed. The torsional vibration resulting from torque and speed fluctuations increases the rattle noise in the gearbox and it should be controlled or minimized in order to gain acceptance by clients and manufactures. The fact that the proprieties of the torsional damper integrated into the clutch disc alter the dynamic characteristic of the system is important in the automotive industry for design purposes. In this study, bench test results for the characteristics of a torsional damper for a clutch system (torsional stiffness and friction moment) and powertrain torsional vibration measurements taken in a passenger car were used to verify and calibrate the model. The adjusted model estimates the driveline natural frequency and the time response vibration. The analysis uses order tracking signal processing to isolate the response from the engine excitation (second-order). It is shown that a decrease in the stiffness of the clutch disc torsional damper lowers the natural frequency and an increase in the friction moment reduces the peak amplitude of the gearbox torsional vibration. The formulation and model adjustment showed that a nonlinear model with three degrees of freedom can represent satisfactorily the powertrain dynamics of a front-wheel drive passenger car.

COMPARATIVE KINEMATIC ANALYSIS OF THE RANGE OF MOVEMENT OF A NORMAL HUMAN KNEE JOINT, STANDARD ARTIFICIAL KNEE AND NOVEL ARTIFICIAL HIGH FLEXION KNEE

2010 ◽  
Vol 22 (01) ◽  
pp. 41-45
Author(s):  
Sam Prasanna Rajkumar ◽  
Sudesh Sivarasu ◽  
Lazar Mathew
Keyword(s):  
Knee Joint ◽  
Range Of Motion ◽  
Degrees Of Freedom ◽  
Range Of Movement ◽  
High Flexion ◽  
Additional Degree ◽  
Normal Knee ◽  
Standard Version ◽  
Knee Movement ◽  
Human Knee Joint

Total Knee Arthroplasty (TKA) using standard artificial knee implant has a limitation in restriction in the range of motion and freedom of movements'. This study was worked out to compare the kinematics of a reconstructed 3D knee with standard and high flexion artificial knee designs. A CT bone model reconstructed with MIMICS for a 3D normal knee joint and the simulation was done for normal knee, standard version of artificial knee as well as the high flexion knee designs. The results of the analyses, provides us an insight that high flexion designs were most suited and gives increased range of motion and also provides an additional degree of freedom so that it almost mimics the normal knee movement. The high flexion design when tested under simulated environment provided a better functionality and increased movements. It was concluded that the normal knee has 6 degrees of freedom (DOF); the standard version has 1 rotation and 1 translation. The high flexion design provides 2 rotations and 1 translation.

Towards an Energy-Based Linear Analysis of Nonholonomic Systems

1999 ◽  
Author(s):  
Marwan Bikdash ◽  
Richard A. Layton
Keyword(s):  
Steady State ◽  
Singular Systems ◽  
Nonholonomic Constraints ◽  
Nonholonomic Systems ◽  
Linear Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Indirect Approach ◽  
Physical Systems ◽  
Future Work

Abstract Guidelines toward an energy-based, linear analysis of discrete physical systems are presented, based on previous work in systematic modeling using Lagrangian differential-algebraic equations (DAEs). Recent work in this area is extended by accommodating nonholonomic constraints and explicit inputs. An equilibrium postulate is proposed and equilibrium is characterized for static and steady-state conditions. Lagrangian DAEs are linearized using a local, indirect approach. Alternate descriptor formulations leading to different linear singular systems are compared and one formulation is determined to be a good foundation for future work in linear analysis using Lagrangian DAEs.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

A Frequency Domain Technique for Characterizing Nonlinearities in a Tire-Vehicle Suspension System

2005 ◽  
Vol 127 (1) ◽  
pp. 61-76 ◽  
Author(s):  
C. Gavin McGee ◽  
Muhammad Haroon ◽  
Douglas E. Adams ◽  
Yiu Wah Luk
Keyword(s):  
Degrees Of Freedom ◽  
A Priori ◽  
Coherence Function ◽  
Suspension System ◽  
Nonlinear Frequency ◽  
Response Measurement ◽  
Nonlinear Characterization ◽  
Experimental Laboratory ◽  
Vehicle Suspension System

Characterization of tire and suspension system nonlinearities in measured data is the first step in developing input-output quarter car models; however, system identification procedures, which require a priori knowledge of all nonlinearities within a system, often receive more attention in the research community. Furthermore, relatively few investigations have focused on nonlinear characterization and identification in the absence of input measurements. A new method for characterizing nonlinearities, in the absence of an input measurement, using transmissibility functions and ordinary coherence functions between response measurement degrees of freedom is discussed here. It is shown that the nonlinear nature of a vehicle system provides information about the nominal linear system when the input is unknown. Nonlinear frequency permutations, which create drops in the ordinary coherence function, serve to characterize the associated nonlinearities. In the absence of input measurements, coherence functions of the response transmissibility between the vehicle spindle and body allow the nonlinearities in the suspension system, but not the tires, to be characterized. Simulation results are discussed and the method is applied to experimental laboratory and operating data to validate the approach.

Stick–Slip Motion of the Chaplygin Sleigh With a Piecewise-Smooth Nonholonomic Constraint

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
Vitaliy Fedonyuk ◽  
Phanindra Tallapragada
Keyword(s):  
Nonholonomic Constraint ◽  
Nonholonomic Constraints ◽  
Piecewise Smooth ◽  
Nonsmooth Dynamics ◽  
Chaplygin Sleigh ◽  
Stick Slip ◽  
Velocity Decay ◽  
Asymptotic Speed ◽  
Asymptotic Motion ◽  
Stick Slip Motion

The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints. Such constraints often arise due to the role of a no-slip requirement imposed by friction. In the case of the Chaplygin sleigh, it is well known that its asymptotic motion is that of pure translation along a straight line. Any perturbations in angular velocity decay and result in an increase in asymptotic speed of the sleigh. Such motion of the sleigh is under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum value to the friction. The Chaplygin sleigh is then under a piecewise-smooth nonholonomic constraint and transitions between “slip” and “stick” modes. We investigate these transitions and the resulting nonsmooth dynamics of the system. We show that the reduced state space of the system can be partitioned into sets of distinct dynamics and that the stick–slip transitions can be explained in terms of transitions of the state of the system between these sets.

Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers

Science ◽  
2013 ◽  
Vol 340 (6140) ◽  
pp. 1545-1548 ◽  
Author(s):  
Nenad Bozinovic ◽  
Yang Yue ◽  
Yongxiong Ren ◽  
Moshe Tur ◽  
Poul Kristensen ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Optical Fiber ◽  
Orbital Angular Momentum ◽  
Degrees Of Freedom ◽  
Nonlinear Effects ◽  
Data Traffic ◽  
Additional Degree ◽  
Mode Division Multiplexing ◽  
Spatial Modes ◽  
Momentum Mode

Internet data traffic capacity is rapidly reaching limits imposed by optical fiber nonlinear effects. Having almost exhausted available degrees of freedom to orthogonally multiplex data, the possibility is now being explored of using spatial modes of fibers to enhance data capacity. We demonstrate the viability of using the orbital angular momentum (OAM) of light to create orthogonal, spatially distinct streams of data-transmitting channels that are multiplexed in a single fiber. Over 1.1 kilometers of a specially designed optical fiber that minimizes mode coupling, we achieved 400-gigabits-per-second data transmission using four angular momentum modes at a single wavelength, and 1.6 terabits per second using two OAM modes over 10 wavelengths. These demonstrations suggest that OAM could provide an additional degree of freedom for data multiplexing in future fiber networks.

Traversability Analysis of a Novel One-DOF Robotic Leg

2013 ◽  
Author(s):  
Lionel Birglen ◽  
Carlos Ruella
Keyword(s):  
Degrees Of Freedom ◽  
Mobile Robotics ◽  
Simulation Algorithm ◽  
Novel Technique ◽  
The Past ◽  
Robotic Leg ◽  
Leg Design ◽  
First Time

In legged mobile robotics the most common approach is to design fully actuated legs with several degrees of freedom (DOF) in order to successfully navigate through rough terrains. However, simpler leg architectures with as few as one-DOF have been developed in the past to achieve the very same goal. The ability of these simpler legs to traverse uneven terrains is arguably limited with respect to multi-DOF designs, but in some applications the reduction of the DOF and hence, of the number of actuators, as well as the simplicity of the associated control could be a great advantage and the decisive argument. In this paper, the authors propose a novel one-DOF robotic leg that has been specially designed to achieve the greatest robustness possible with respect to the difficult terrains it has to traverse. In order to do that, a method to analyze and optimize any one-DOF robotic leg with respect to its ability to overcome obstacles is proposed here. This method is based on a simple and efficient novel technique to generate synthetic terrains combined with a simulation algorithm estimating the traversability of the particular one-DOF leg design under scrutiny. To illustrate the generality of the proposed method, it is used to design both an optimal leg with the architecture presented here for the first time and also, one with the most common one-DOF leg architecture found in the literature.

scholarly journals On-Sun Tracking Evaluation of a Small-Scale Tensile Ganged Heliostat Prototype

2019 ◽  
Author(s):  
Julius Yellowhair ◽  
Kenneth M. Armijo ◽  
Jesus D. Ortega ◽  
Jim Clair
Keyword(s):  
Degrees Of Freedom ◽  
Small Scale ◽  
Preliminary Evaluation ◽  
Control Mechanisms ◽  
Tracking Accuracy ◽  
Additional Degree ◽  
Number Of Components ◽  
The Past ◽  
Linear Actuators ◽  
The Individual

Abstract Various ganged heliostat concepts have been proposed in the past. The attractive aspect of ganged heliostat concepts is multiple heliostats are grouped so that pedestals, tracking drives, and other components can be shared, thus reducing the number of components. The reduction in the number of components is thought to significantly reduce cost. However, since the drives and tracking mechanisms are shared, accurate on-sun tracking of grouped heliostats becomes challenging because the angular degrees-of-freedom are now limited for the multiple number of combined heliostats. In this paper, the preliminary evaluation of the on-sun tracking of a novel tensile-based cable suspended ganged heliostat concept is provided. In this concept, multiple heliostats are attached to two guide cables. The cables are attached to rotation spreader arms which are anchored to end posts on two ends. The guide cables form a catenary which makes tracking on-sun interesting and challenging. Tracking is performed by rotating the end plates that the two cables are attached to and rotating the individual heliostats in one axis. An additional degree-of-freedom can be added by differentially tensioning the two cables, but this may be challenging to do in practice. Manual on-sun tracking was demonstrated on small-scale prototypes. The rotation arms were coarsely controlled with linear actuators, and the individual heliostats were hand-adjusted in local pitch angle and locked in place with set screws. The coarse angle adjustments showed the tracking accuracy was 3–4 milli-radians. However, with better angle control mechanisms the tracking accuracy can be drastically improved. In this paper, we provide tracking data that was collected for a day, which showed feasibility for automated on-sun tracking. The next steps are to implement better angle control mechanisms and develop tracking algorithms so that the ganged heliostats can automatically track.

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