A Slinky’s Elastic Potential Energy

2020 ◽  
Vol 58 (3) ◽  
pp. 198-199
Author(s):  
Philip Gash
Keyword(s):  
Potential Energy ◽  
Elastic Potential ◽  
Elastic Potential Energy

An Accurate and Robust Geometrically Exact Curved Beam Formulation for Multibody Dynamic Analysis

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
H. Ren ◽  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Potential Energy ◽  
Cross Section ◽  
Small Strain ◽  
Elastic Potential ◽  
Rotation Vector ◽  
Benchmark Problems ◽  
Position Vector ◽  
Current Formulation ◽  
Geometrically Exact Beam ◽  
Elastic Potential Energy

An accurate and robust geometrically exact beam formulation (GEBF) is developed to simulate the dynamics of a beam with large deformations and large rotations. The undeformed configuration of the centroid line of the beam can be either straight or curved, and cross sections of the beam can be either uniform or nonuniform with arbitrary shapes. The beam is described by the position of the centroid line and a local frame of a cross section, and a rotation vector is used to characterize the rotation of the cross section. The elastic potential energy of the beam is derived using continuum mechanics with the small-strain assumption and linear constitutive relation, and a factor naturally arises in the elastic potential energy, which can resolve a drawback of the traditional GEBF. Shape functions of the position vector and rotation vector are carefully chosen, and numerical incompatibility due to independent discretization of the position vector and rotation vector is resolved, which can avoid the shear locking problem. Numerical singularity of the rotation vector with its norm equal to zero is eliminated by Taylor polynomials. A rescaling strategy is adopted to resolve the singularity problem with its norm equal to 2mπ, where m is a nonzero integer. The current formulation can be used to handle linear and nonlinear dynamics of beams under arbitrary concentrated and distributed loads. Several benchmark problems are simulated using the current formulation to validate its accuracy, adaptiveness, and robustness.

A Kinematic Comparison of Spring-Loaded and Traditional Crutches

2011 ◽  
Vol 20 (2) ◽  
pp. 198-206 ◽  
Author(s):  
Matthew K. Seeley ◽  
Iain Hunter ◽  
Thomas Bateman ◽  
Adam Roggia ◽  
Brad J. Larson ◽  
...  
Keyword(s):  
Potential Energy ◽  
Outcome Measures ◽  
High Speed ◽  
Elastic Potential ◽  
Ground Contact ◽  
Type Design ◽  
Additional Peak ◽  
Dependent Variables ◽  
Elastic Potential Energy ◽  
Independent Variable

Context:A novel spring-loaded-crutch design may provide patients additional forward velocity, relative to traditional axillary crutches; however, this idea has not yet been evaluated.Objective:To quantify elastic potential energy stored by spring-loaded crutches during crutch–ground contact and determine whether this energy increases forward velocity for patients during crutch ambulation. Because elastic potential energy is likely stored by the spring-loaded crutch during ambulation, the authors hypothesized that subjects would exhibit greater peak instantaneous forward velocity during crutch–ground contact and increased preferred ambulation speed during spring-loaded-crutch ambulation, relative to traditional-crutch ambulation.Design:Within-subject.Setting:Biomechanics laboratory.Participants:10 healthy men and 10 healthy women.Interventions:The independent variable was crutch type: Subjects used spring-loaded and traditional axillary crutches to ambulate at standardized and preferred speeds.Main Outcome Measures:The primary dependent variables were peak instantaneous forward velocity and preferred ambulation speed; these variables were quantified using high-speed videography and an optoelectronic timing device, respectively. Between-crutches differences for the dependent variables were evaluated using paired t tests (α = .05). Elastic potential energy stored by the spring-loaded crutches during crutch–ground contact was also quantified via videography.Results:Peak forward velocity during crutch–ground contact was 5% greater (P < .001) for spring-loaded-crutch ambulation than for traditional-crutch ambulation. Preferred ambulation speed, however, did not significantly differ (P = .538) between crutch types. The spring-loaded crutches stored an average of 2.50 ± 1.96 J of elastic potential energy during crutch–ground contact.Conclusions:The spring-loaded crutches appear to have provided subjects with additional peak instantaneous forward velocity. This increased velocity, however, was relatively small and did not increase preferred ambulation speed.

A Model for Quantifying System Evolvability Based on Excess and Capacity

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Morgan W. P. Tackett ◽  
Christopher A. Mattson ◽  
Scott M. Ferguson
Keyword(s):  
Potential Energy ◽  
Design Process ◽  
Elastic Potential ◽  
Aircraft Carrier ◽  
Elastic Potential Energy ◽  
Engineered Systems ◽  
Mathematical Relationships ◽  
Service Building

An important factor in system longevity is service-phase evolvability, which is defined as the ability of a system to physically transform from one configuration to a more desirable configuration while in service. These transformations may or may not be known during the design process, and may or may not be reversible. In a different study, we examined 210 engineered systems and found that system excess and modularity allow a system to evolve while in service. Building on this observation, the present paper introduces mathematical relationships that map a system's excess to that system's ability to evolve. As introduced in this paper, this relationship is derived from elastic potential-energy theories. The use of the evolvability measure, and other related measures presented herein, are illustrated with simple examples and applied to the design of U.S. Navy nuclear aircraft carriers. Using these relationships, we show that the Navy's new Ford-class aircraft carrier is measurably more evolvable than the Nimitz-class carriers. While the ability for systems to evolve is based on excess and modularity, this paper is focused only on excess. The mapping between modularity and evolvability is the focus of another work by the authors.

On the Perfect Gravity-Balance of a Spatial N-DOF Manipulator Based on the Localized Pseudo-Base

2009 ◽  
Author(s):  
Po-Yang Lin ◽  
Win-Bin Shieh ◽  
Dar-Zen Chen
Keyword(s):  
Exact Solution ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Rotation Axis ◽  
Industrial Robot ◽  
Elastic Potential ◽  
Gravitational Potential Energy ◽  
Mass Center ◽  
Elastic Potential Energy ◽  
Six Dof

This paper offers an exact solution for the perfect gravity-balance of a class of spatial manipulators with no translational joints. The methodology used is based on the concept of conservation of the gravitational and elastic potential energy of the system. The overall gravitational potential energy of a serial-connected, n-link manipulator is identified to be contributed by n subsystems, where each subsystem is kinematically equivalent to one of the primary links of the manipulator, and possesses the accumulated mass of its post-connected links with a fixed mass center located on the subsystem. The gravitational potential energy of such a subsystem can be fully balanced by the elastic potential energy of the spring fitted between the link and its adjacent pseudo-base. Since the rotation axis of the pseudo-base is required to be in the direction of gravity, n serial-connected RSSR modules are constituted along the primary chain of the manipulator to provide a pseudo-base for each of the primary links. With one linear, zero-free-length spring fitted between each of the primary links of the manipulator and its associated pseudo-base, a static equilibrium of the considered mechanism in any configuration can be reached. A numerical example of the model of a six-DOF industrial robot has demonstrated the success of the proposed methodology.

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