Dynamic Analysis of Rectilinear Motion of a Self-Propelling Disk With Unbalance Masses

2000 ◽  
Vol 68 (1) ◽  
pp. 58-66 ◽  
Author(s):  
T. Das ◽  
R. Mukherjee
Keyword(s):  
Potential Energy ◽  
Dynamic Model ◽  
Center Of Mass ◽  
Static Model ◽  
Rectilinear Motion ◽  
Constant Acceleration ◽  
Physical Constraints ◽  
Straight Line ◽  
Radial Spokes ◽  
The Masses

This paper investigates the dynamics of a rolling disk with three unbalance masses that can slide along radial spokes equispaced in angular orientation. The objective is to design trajectories for the masses that satisfy physical constraints and enable the disk to accelerate or move with constant velocity. The disk is designed to remain vertically upright and is constrained to move along a straight line. We design trajectories for constant acceleration, first using a static model, and then through detailed analysis using a dynamic model. The analysis based on the dynamic model considers two separate cases; one where the potential energy of the system is conserved, and the other where it continually varies. Whereas trajectories conserving potential energy are quite similar to those obtained from the static model, the variable potential energy trajectories are the most general. A number of observations related to the system center-of-mass are made with respect to both trajectories. Following the strategy for constant acceleration maneuvers, we give a simple approach to tracking an acceleration profile and provide some simulation results.

Dynamics of a Self-Propelling Wheel With Three Eccentric Masses

2000 ◽  
Author(s):  
Tuhin K. Das ◽  
Ranjan Mukherjee
Keyword(s):  
Potential Energy ◽  
Constant Velocity ◽  
Simple Approach ◽  
Constant Acceleration ◽  
Physical Constraints ◽  
Straight Line ◽  
Radial Spokes ◽  
Simulation Results ◽  
The Masses ◽  
Variable Potential

Abstract This paper investigates the dynamics of a rolling disk with three unbalance masses that can slide along radial spokes equispaced in angular orientation. The objective is to design trajectories for the masses that satisfy physical constraints and enable the disk to accelerate or move with constant velocity. The disk is designed to remain vertically upright and is constrained to move along a straight line. We design trajectories for constant acceleration through detailed analysis using a dynamic model. The analysis considers two separate cases; one where the potential energy of the system is conserved, and the other where it continually varies. Whereas trajectories conserving potential energy are limacons, the variable potential energy trajectories are the most general and allow greater acceleration. Following the strategy for constant acceleration maneuvers, we give a simple approach to tracking an acceleration profile and provide simulation results.

scholarly journals Ocean Convective Available Potential Energy. Part II: Energetics of Thermobaric Convection and Thermobaric Cabbeling

2016 ◽  
Vol 46 (4) ◽  
pp. 1097-1115 ◽  
Author(s):  
Zhan Su ◽  
Andrew P. Ingersoll ◽  
Andrew L. Stewart ◽  
Andrew F. Thompson
Keyword(s):  
Potential Energy ◽  
Deep Convection ◽  
Center Of Mass ◽  
Convective Available Potential Energy ◽  
Vertical Mixing ◽  
Available Potential Energy ◽  
Energy Part ◽  
Different Temperatures ◽  
Simplifying Assumptions ◽  
Diabatic Processes

AbstractThe energetics of thermobaricity- and cabbeling-powered deep convection occurring in oceans with cold freshwater overlying warm salty water are investigated here. These quasi-two-layer profiles are widely observed in wintertime polar oceans. The key diagnostic is the ocean convective available potential energy (OCAPE), a concept introduced in a companion piece to this paper (Part I). For an isolated ocean column, OCAPE arises from thermobaricity and is the maximum potential energy (PE) that can be converted into kinetic energy (KE) under adiabatic vertical parcel rearrangements. This study explores the KE budget of convection using two-dimensional numerical simulations and analytical estimates. The authors find that OCAPE is a principal source for KE. However, the complete conversion of OCAPE to KE is inhibited by diabatic processes. Further, this study finds that diabatic processes produce three other distinct contributions to the KE budget: (i) a sink of KE due to the reduction of stratification by vertical mixing, which raises water column’s center of mass and thus acts to convert KE to PE; (ii) a source of KE due to cabbeling-induced shrinking of the water column’s volume when water masses with different temperatures are mixed, which lowers the water column’s center of mass and thus acts to convert PE into KE; and (iii) a reduced production of KE due to diabatic energy conversion of the KE convertible part of the PE to the KE inconvertible part of the PE. Under some simplifying assumptions, the authors also propose a theory to estimate the maximum depth of convection from an energetic perspective. This study provides a potential basis for improving the convection parameterization in ocean models.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

scholarly journals Turning Gait Planning Method for Humanoid Robots

2018 ◽  
Vol 8 (8) ◽  
pp. 1257 ◽  
Author(s):  
Tianqi Yang ◽  
Weimin Zhang ◽  
Xuechao Chen ◽  
Zhangguo Yu ◽  
Libo Meng ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Translational Motion ◽  
Humanoid Robots ◽  
Inverted Pendulum Model ◽  
Straight Line ◽  
Pendulum Model ◽  
The Stability ◽  
And Control ◽  
Present Simulation

The most important feature of this paper is to transform the complex motion of robot turning into a simple translational motion, thus simplifying the dynamic model. Compared with the method that generates a center of mass (COM) trajectory directly by the inverted pendulum model, this method is more precise. The non-inertial reference is introduced in the turning walk. This method can translate the turning walk into a straight-line walk when the inertial forces act on the robot. The dynamics of the robot model, called linear inverted pendulum (LIP), are changed and improved dynamics are derived to make them apply to the turning walk model. Then, we expend the new LIP model and control the zero moment point (ZMP) to guarantee the stability of the unstable parts of this model in order to generate a stable COM trajectory. We present simulation results for the improved LIP dynamics and verify the stability of the robot turning.

scholarly journals 2. On the Law of Inertia; the Principle of Chronometry; and the Principle of Absolute Clinural Rest, and of Absolute Rotation

1884 ◽  
Vol 12 ◽  
pp. 568-578 ◽  
Author(s):  
James Thomson
Keyword(s):  
Rectilinear Motion ◽  
Straight Line ◽  
The Law ◽  
The Universe

There is no distinction known to men among states of existence of a body which can give reason for any one state being regarded as a state of absolute rest in space, and any other being regarded as a state of uniform rectilinear motion. Men have no means of knowing, nor even of imagining, any one length rather than any other, as being the distance between the place occupied by the centre of a ball at present, and the place that was occupied by that centre at any past instant; nor of knowing or imagining any one direction, rather than any other, as being the direction of the straight line from the former place to the new place, if the ball is supposed to have been moving in space. The point of space that was occupied by the centre of the ball at any specifiod past moment is utterly lost to us as soon as that moment is past, or as soon as the centre has moved out of that point, having left no trace recognisable by us of its past place in the universe of space.

A Dynamic Assembly Modeling Method for Satellite Final Assembly Sequence Planning

2010 ◽  
Vol 156-157 ◽  
pp. 332-338
Author(s):  
Yuan Zhang ◽  
Kai Fu Zhang ◽  
Jian Feng Yu ◽  
Lei Zhao
Keyword(s):  
Dynamic Model ◽  
Static Model ◽  
Modeling Method ◽  
Assembly Sequence Planning ◽  
Assembly Model ◽  
Assembly Sequence ◽  
Final Assembly ◽  
Model Tree ◽  
Assembly Sequences ◽  
Dynamic Assembly

To study the effect of assembly process information combining disassemble and assemble on satellite assembly sequence, this paper presents an object-oriented and assembly information integrated model, which is composed of static model and dynamic model. The feasibility determination based on Cut-set theory is presented and the construction algorithm of dynamic model is established by static model, the dynamic assembly model tree is obtained by analyzing in layers and verifying possible states using this algorithm, where the assembly model tree includes all the geometric feasible assembly sequences of satellite. Finally, this modeling method is verified by a satellite product.

Corporate governance mechanisms and corporate investments: evidence from India

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Samridhi Suman ◽  
Shveta Singh
Keyword(s):  
Corporate Governance ◽  
Dynamic Model ◽  
Capital Expenditure ◽  
Agency Problem ◽  
Agency Problems ◽  
Static Model ◽  
Capital Expenditures ◽  
Content Type ◽  
Empire Building ◽  
The Impact

PurposeThe purpose of this paper is to empirically investigate the influence of corporate governance variables relating to the board of directors, audit and ownership on the agency problems that inflict a firm's investments in capital and research and development (R&D) expenditures. This study posits that the R&D investments are inflicted by the agency problem of “quiet life” whereas “empire-building” agency problem affects capital expenditure decisions.Design/methodology/ approachThis study analyses the investment behaviour of non-financial and non-utility firms listed on NIFTY 200 from FY 2009 to FY 2018 using a static and dynamic model.FindingsThe results from the static model suggest that ownership concentration mitigates the agency problem of the “quiet life” that affects R&D expenditures. However, no corporate governance attribute has a significant impact on R&D investments under the assumption of the dynamic model. In respect of capital expenditures, the analysis of static model yields that audits by large auditor firms and usage of non-audit services ameliorate the agency problem of “empire-building”. The results from the dynamic model show that independent boards worsen it. They also continue to provide empirical evidence in favour of large auditors.Originality/valueThis paper contributes to the literature on the corporate governance-investment association by simultaneously examining the impact of multiple corporate governance attributes on the agency problems of “quiet life” and “empire-building” that affect R&D and capital expenditures, respectively, in a static and dynamic context for a sample of Indian firms.

Utility of Matrix Algebra and Graphical User Interface in Design of Six-Bar Mechanism for Rectilinear Motion Generation

2013 ◽  
Author(s):  
Behrooz Fallahi ◽  
Seyyed Alireza Seyyed Mousavi ◽  
Arjun Kumar Perla ◽  
Ilia Mokhtarian
Keyword(s):  
User Interface ◽  
Graphical User Interface ◽  
Matrix Algebra ◽  
Design Space ◽  
Rectilinear Motion ◽  
Motion Generation ◽  
Straight Line ◽  
Synthesis Procedure ◽  
And Inversion

Many applications require design of a linkage that executes a rectilinear motion. In this study a synthesis procedure for six-bar mechanism for generation of rectilinear motion is presented. To achieve this goal, matrix algebra is used to describe translation, rotation, and inversion of motion of links. These concepts then are used to implement the classical three-precision point synthesize of a four-bar mechanism with a coupler point that traces a straight line. The motion of this four-bar mechanism is inverted and then is used to synthesize a second four-bar mechanism. The merging of these two four-bar mechanisms forms a six-bar mechanism such that the motion of one link is rectilinear motion. To implement this procedure, a graphical user interface is developed for the ease of exploring the design space. The utility of this approach is demonstrated by designing a linkage for a lift-truck.

Reducing the metabolic rate of walking and running with a versatile, portable exosuit

Science ◽  
2019 ◽  
Vol 365 (6454) ◽  
pp. 668-672 ◽  
Author(s):  
Jinsoo Kim ◽  
Giuk Lee ◽  
Roman Heimgartner ◽  
Dheepak Arumukhom Revi ◽  
Nikos Karavas ◽  
...  
Keyword(s):  
Potential Energy ◽  
Metabolic Rate ◽  
Athletic Performance ◽  
Center Of Mass ◽  
Treadmill Walking ◽  
Metabolic Rates ◽  
Hip Extension ◽  
Uphill Walking

Walking and running have fundamentally different biomechanics, which makes developing devices that assist both gaits challenging. We show that a portable exosuit that assists hip extension can reduce the metabolic rate of treadmill walking at 1.5 meters per second by 9.3% and that of running at 2.5 meters per second by 4.0% compared with locomotion without the exosuit. These reduction magnitudes are comparable to the effects of taking off 7.4 and 5.7 kilograms during walking and running, respectively, and are in a range that has shown meaningful athletic performance changes. The exosuit automatically switches between actuation profiles for both gaits, on the basis of estimated potential energy fluctuations of the wearer’s center of mass. Single-participant experiments show that it is possible to reduce metabolic rates of different running speeds and uphill walking, further demonstrating the exosuit’s versatility.

scholarly journals The Possibility of Zero Limb-Work Gaits in Sprawled and Parasagittal Quadrupeds: Insights from Linkages of the Industrial Revolution

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
J R Usherwood
Keyword(s):  
Potential Energy ◽  
Industrial Revolution ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Phase Fluctuation ◽  
Vertical Axis ◽  
The Body ◽  
Mechanical Work ◽  
Gravitational Potential Energy ◽  
Pull Out

Synopsis Animal legs are diverse, complex, and perform many roles. One defining requirement of legs is to facilitate terrestrial travel with some degree of economy. This could, theoretically, be achieved without loss of mechanical energy if the body could take a continuous horizontal path supported by vertical forces only—effectively a wheel-like translation, and a condition closely approximated by walking tortoises. If this is a potential strategy for zero mechanical work cost among quadrupeds, how might the structure, posture, and diversity of both sprawled and parasagittal legs be interpreted? In order to approach this question, various linkages described during the industrial revolution are considered. Watt’s linkage provides an analogue for sprawled vertebrates that uses diagonal limb support and shows how vertical-axis joints could enable approximately straight-line horizontal translation while demanding minimal mechanical power. An additional vertical-axis joint per leg results in the wall-mounted pull-out monitor arm and would enable translation with zero mechanical work due to weight support, without tipping or toppling. This is consistent with force profiles observed in tortoises. The Peaucellier linkage demonstrates that parasagittal limbs with lateral-axis joints could also achieve the zero-work strategy. Suitably tuned four-bar linkages indicate this is feasibly approximated for flexed, biologically realistic limbs. Where “walking” gaits typically show out of phase fluctuation in center of mass kinetic and gravitational potential energy, and running, hopping or trotting gaits are characterized by in-phase energy fluctuations, the zero limb-work strategy approximated by tortoises would show zero fluctuations in kinetic or potential energy. This highlights that some gaits, perhaps particularly those of animals with sprawled or crouched limbs, do not fit current kinetic gait definitions; an additional gait paradigm, the “zero limb-work strategy” is proposed.

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