Planar and Spatial Gravity Balancing With Normal Springs

2004 ◽  
Author(s):  
Freek L. S. te Riele ◽  
Edsko E. G. Hekman ◽  
Just L. Herder
Keyword(s):  
Potential Energy ◽  
Inverted Pendulum ◽  
Design Synthesis ◽  
Free Length ◽  
Energy Consideration ◽  
Complex Mechanisms ◽  
Balancing Conditions ◽  
The Ideal

Very often, spring-to-gravity-balancing mechanisms are conceived with ideal (zero-free-length l0=0) springs. However, the use of ideal springs in the conception phase tends to lead to more complex mechanisms because the ideal spring functionality has to be approximated with normal springs. To facilitate construction of (gravity) balancers, employing normal springs (l0≠0) directly mounted between the link attachment points of the mechanism in the conception phase therefore seems beneficiary. This paper discusses spring mechanisms that enable perfect balancing of gravity acting on an inverted pendulum while employing normal springs between the spring-attachment points: The design synthesis of such mechanisms will be explained and balancing conditions will be derived, using a potential energy consideration.

Spatial Static Gravity Balancing With Ideal Springs

2004 ◽  
Author(s):  
Freek L. S. te Riele ◽  
Just L. Herder ◽  
Edsko E. G. Hekman
Keyword(s):  
Potential Energy ◽  
Inverted Pendulum ◽  
Spherical Joint ◽  
Static Balancing ◽  
Energy Expression ◽  
Energy Consideration ◽  
Balancing Conditions ◽  
Spring Mechanism ◽  
Potential Energy Expression

This paper discusses mechanisms that allow for perfect static balancing of rotations about a fixed spherical joint by means of ideal springs. Using a potential energy consideration, balancing conditions of a spatial three-spring balancer will be derived. It will be shown that not satisfying these conditions causes non-constant terms in the potential energy expression of the spring-mechanism, which can be eliminated by coupling the spring-mechanism to an inverted pendulum.

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.

Synthesized ADRC for One-Level Inverted Pendulum System through Combination of Separating and Assembling

2014 ◽  
Vol 490-491 ◽  
pp. 794-797
Author(s):  
Wen Ping Li ◽  
Li Qiang Wu
Keyword(s):  
Nonlinear System ◽  
Inverted Pendulum ◽  
Dynamical Decoupling ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Strong Robustness ◽  
Ideal Study ◽  
Simulation Results ◽  
The One ◽  
The Ideal

Inverted pendulum system is the ideal study object of nonlinear system. The ADRC has good estimate for disturbances, strong robustness and using static decoupling instead of dynamical decoupling. The one-level inverted pendulum system can be regarded as composing of the pendulum angel system and the cart position system. The former is faster and the later is slower. The synthesized ADRC for one-level inverted pendulum system is built through combination of separating and assembling to reduce difficulty in optimizing ADRC parameters of the inverted pendulum system. The synthesized controller is simulated by Matlab under different parameters of the inverted pendulum. Simulation results show that the pendulum angle and the cart position are well controlled.

Mechanics of locomotion in lizards.

1997 ◽  
Vol 200 (16) ◽  
pp. 2177-2188 ◽  
Author(s):  
C T Farley ◽  
T C Ko
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Gravitational Potential Energy ◽  
Lateral Bending ◽  
Walking Gait ◽  
Bending Force

Lizards bend their trunks laterally with each step of locomotion and, as a result, their locomotion appears to be fundamentally different from mammalian locomotion. The goal of the present study was to determine whether lizards use the same two basic gaits as other legged animals or whether they use a mechanically unique gait due to lateral trunk bending. Force platform and kinematic measurements revealed that two species of lizards, Coleonyx variegatus and Eumeces skiltonianus, used two basic gaits similar to mammalian walking and trotting gaits. In both gaits, the kinetic energy fluctuations due to lateral movements of the center of mass were less than 5% of the total external mechanical energy fluctuations. In the walking gait, both species vaulted over their stance limbs like inverted pendulums. The fluctuations in kinetic energy and gravitational potential energy of the center of mass were approximately 180 degrees out of phase. The lizards conserved as much as 51% of the external mechanical energy required for locomotion by the inverted pendulum mechanism. Both species also used a bouncing gait, similar to mammalian trotting, in which the fluctuations in kinetic energy and gravitational potential energy of the center of mass were nearly exactly in phase. The mass-specific external mechanical work required to travel 1 m (1.5 J kg-1) was similar to that for other legged animals. Thus, in spite of marked lateral bending of the trunk, the mechanics of lizard locomotion is similar to the mechanics of locomotion in other legged animals.

scholarly journals On the Design Synthesis of Multistable Equilibrium Systems

2004 ◽  
Author(s):  
Carey W. King ◽  
Matthew I. Campbell ◽  
Joseph J. Beaman
Keyword(s):  
Potential Energy ◽  
Potential Energy Curve ◽  
Optimization Methods ◽  
Energy Curve ◽  
Stable Configuration ◽  
Stable States ◽  
Design Synthesis ◽  
Performance Space ◽  
Equilibrium Configurations ◽  
A Performance

Multistable equilibrium (MSE) systems are a type of adaptable system that can have multiple mechanical configurations requiring no power to maintain the stable configurations. Thus, power is only needed to move among the stable states, and each stable configuration represents a level of adaptability. Since stable equilibrium configurations can be defined by potential energy minima, we base the design of MSE systems on shaping the potential energy curve at desired equilibrium configurations. This view allows one to construct a performance space defined by how well candidate systems meet a desired potential energy curve. By using a Monte Carlo mapping to link the performance space to the design space in tandem with stochastic optimization methods, the designer determines whether or not a certain system topology can be designed as a MSE system. Qualitative and quantitative mapping procedures enable the designer to decide whether or not the desired design lies near the center or periphery of a performance space. This dictates how the optimization is to be executed which in turn informs the designer as to whether or not a feasible limit in the system performance has indeed been reached.

Spring-to-Spring Balancing as Energy-Free Adjustment Method in Gravity Equilibrators

2009 ◽  
Author(s):  
Rogier Barents ◽  
Mark Schenk ◽  
Wouter D. van Dorsser ◽  
Boudewijn M. Wisse ◽  
Just L. Herder
Keyword(s):  
Potential Energy ◽  
Adjustment Method ◽  
Free Length ◽  
Regular Extension ◽  
Conceptual Designs ◽  
Constant Potential ◽  
Spring Mechanism

Generally, adjustment of gravity equilibrator to a new payload requires energy, e.g. to increase the pre-load of the balancing spring. A novel way of energy-free adjustment of gravity equilibrators is possible by introducing the concept of a storage spring. The storage spring supplies or stores the energy necessary to adjust the balancer spring of the gravity equilibrator. In essence the storage spring mechanism maintains a constant potential energy within the spring mechanism; energy is exchanged between the storage and balancer spring when needed. Various conceptual designs using both zero-free-length springs and regular extension springs are proposed. Two models were manufactured demonstrating the practical embodiments and functionality.

scholarly journals Gravity Balancing Conditions for an Upper Arm Exoskeleton

2010 ◽  
Vol 4 (2) ◽  
Author(s):  
Venketesh Dubey ◽  
Sunil Agrawal
Keyword(s):  
Shoulder Joint ◽  
Analytical Study ◽  
Upper Arm ◽  
Functional Training ◽  
Free Length ◽  
Shoulder Joints ◽  
Joint Forces ◽  
Human Arm ◽  
Wearable Exoskeleton ◽  
Balancing Conditions

An upper-arm wearable exoskeleton has been designed for assistance and functional training of humans. One of the goals of this design is to provide passive assistance to a user by gravity balancing, while keeping the transmitted forces to the shoulder joints at a minimum. Consistent with this goal, this paper addresses the following questions: (i) an analytical study of gravity balancing design conditions for the structure of the human arm, (ii) minimization of transmitted shoulder joint forces while satisfying the gravity balancing conditions, and (iii) possible implementation of these conditions into practical designs using zero-free length springs.

Spring-to-Spring Balancing as Energy-Free Adjustment Method in Gravity Equilibrators

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Rogier Barents ◽  
Mark Schenk ◽  
Wouter D. van Dorsser ◽  
Boudewijn M. Wisse ◽  
Just L. Herder
Keyword(s):  
Potential Energy ◽  
Adjustment Method ◽  
Free Length ◽  
Regular Extension ◽  
Conceptual Designs ◽  
Constant Potential ◽  
Spring Mechanism

Generally, adjustment of gravity equilibrators to a new payload requires energy, e.g., to increase the preload of the balancing spring. A novel way of energy-free adjustment of gravity equilibrators is possible by introducing the concept of a storage spring. The storage spring supplies or stores the energy necessary to adjust the balancer spring of the gravity equilibrator. In essence, the storage spring mechanism maintains a constant potential energy within the spring mechanism; energy is exchanged between the storage and the balancer spring when needed. Various conceptual designs using both zero-free-length springs and regular extension springs are proposed. Two models were manufactured demonstrating the practical embodiments and functionality.

Vibration of Nearly Perfect Spring Equilibrators

1997 ◽  
Author(s):  
R. Randall Soper ◽  
Dean T. Mook ◽  
Charles F. Reinholtz
Keyword(s):  
Nonlinear Dynamics ◽  
Range Of Motion ◽  
The Other ◽  
Phase Portraits ◽  
Practical Implementation ◽  
Finite Radius ◽  
Free Length ◽  
Attachment Point ◽  
Wide Range ◽  
The Ideal

Abstract Perfect spring equilibrators balance an eccentric rotating weight over a wide range of motion. The mechanism relies on a spring of zero free length. One practical implementation uses a spring and cable of finite free length wrapped over a pulley located at the grounded spring attachment point of the ideal mechanism. The pulley of finite radius introduces some error in the balancing moment. In this paper the kinematics of a practically implemented perfect spring equilibrator are developed. Two kinematic cases are shown to exist. In one case, the kinematics are periodic in the weight arm rotation. In the other case, the geometry causes the spring cable to wrap or unwrap resulting in non-periodic kinematics. Phase portraits are used to illustrate the nonlinear dynamics of the system. The effect of various parameters are examined.

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