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.

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.

On the Equivalence of the Galerkin and Rayleigh-Ritz Methods

1962 ◽  
Vol 66 (621) ◽  
pp. 592-592 ◽  
Author(s):  
Josef Singer
Keyword(s):  
Approximate Solution ◽  
Potential Energy ◽  
Galerkin Method ◽  
Ritz Method ◽  
Total Potential Energy ◽  
Energy Expression ◽  
Total Potential ◽  
Elasticity Problems ◽  
The Galerkin Method ◽  
Potential Energy Expression

The Galerkin method for the approximate solution of elasticity problems (see e.g. Ref. 1) is usually presented as an alternative to the Rayleigh-Ritz method. The main distinction between the two methods is stated to be that the former begins with an equation of equilibrium, whereas the latter begins with a total potential energy expression. The two methods are not always equivalent, and the conditions for equivalence are given in Duncan's lucid presentation of the method (Refs. 2 and 3, which unfortunately have been out of print for some time). These conditions, however, are generally omitted from discussions of the Galerkin method, and it is the purpose of this note to re-emphasise them in a slightly different form.

A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons

2002 ◽  
Vol 14 (4) ◽  
pp. 783-802 ◽  
Author(s):  
Donald W Brenner ◽  
Olga A Shenderova ◽  
Judith A Harrison ◽  
Steven J Stuart ◽  
Boris Ni ◽  
...  
Keyword(s):  
Potential Energy ◽  
Bond Order ◽  
Second Generation ◽  
Energy Expression ◽  
Rebo Potential ◽  
Potential Energy Expression

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.

Design of Nonlinear Rotational Stiffness Using a Noncircular Pulley-Spring Mechanism

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
Bongsu Kim ◽  
Ashish D. Deshpande
Keyword(s):  
Inverted Pendulum ◽  
Synthesis Method ◽  
Gravity Compensation ◽  
Passive Torque ◽  
Double Exponential ◽  
Torque Generation ◽  
Synthesis Procedure ◽  
Decomposition Experiments ◽  
Spring Mechanism ◽  
The Masses

We present a new methodology for designing a nonlinear rotational spring with a desired passive torque profile by using a noncircular pulley-spring mechanism. A synthesis procedure for the shape of the noncircular pulley is presented. The method is based on an infinitesimal calculus approach that leads to an analytical solution, and the method is extended to address practical design issues related to the cable routing. Based on the synthesis method, an antagonistic spring configuration is designed for bilateral torque generation and is designed such that there is no slack in the routing cables. Two design examples are presented, namely, double exponential torque generation and gravity compensation for an inverted pendulum. Experiments with a mechanism for gravity compensation of an inverted pendulum validate our approach. We extend our approach to generate nonlinear torques at two joints by introducing the concept of torque decomposition. Experiments with a two-link robotic arm show that the gravitational forces from the masses on each link are accurately compensated for with our noncircular pulley-spring mechanisms.

An Optimization Method for the Static Balancing of Manipulators Using Springs

2020 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Potential Energy ◽  
Objective Function ◽  
Multiple Solutions ◽  
Optimization Method ◽  
Total Potential Energy ◽  
Static Balancing ◽  
Attachment Point ◽  
Total Potential

Abstract This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.

Energy-free adjustment of gravity equilibrators by adjusting the spring stiffness

2008 ◽  
Vol 222 (9) ◽  
pp. 1839-1846 ◽  
Author(s):  
W D van Dorsser ◽  
R Barents ◽  
B M Wisse ◽  
M Schenk ◽  
J L Herder
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Spring Stiffness ◽  
External Energy ◽  
Static Balancing ◽  
Concept Model ◽  
Total Potential ◽  
Novel Variant ◽  
Energy Conserving

Static balancing is a useful concept to reduce the operating effort of mechanisms. Spring mechanisms are used to achieve a constant total potential energy, thus eliminating any preferred position. Quasi-statically, the mechanism, once statically balanced, can be moved virtually without the operating energy. In some cases, it is desirable to adjust the characteristic of the balancer, for instance, due to a change in the payload in a gravity balanced mechanism. The adjustment of current static balancers requires significant operating energy. This paper will present a novel variant to adjust the spring- and linkage-based static balancers without the need for external energy. The variant makes use of the possibility to adjust the spring stiffness in an energy-conserving way by adjusting the number of active coils. The conditions under which it functions properly will be given, and a proof of the concept model will be shown.

Static Balancing of Tensegrity Mechanisms

2006 ◽  
Vol 129 (3) ◽  
pp. 295-300 ◽  
Author(s):  
Marc Arsenault ◽  
Clément M. Gosselin
Keyword(s):  
Degree Of Freedom ◽  
Static Balancing ◽  
Equilibrium Configurations ◽  
Balancing Conditions ◽  
Three Degree Of Freedom

The computation of the equilibrium configurations of tensegrity mechanisms is often a very tedious task even for relatively simple architectures. However, it has been observed that the complexity of this problem is significantly reduced when gravitational loads are compensated with the use of static balancing techniques. In this work, the general static balancing conditions are adapted for the case of tensegrity mechanisms. Afterward, the modified conditions are applied to two new spatial three-degree-of-freedom tensegrity mechanisms.

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.

Static Balancing of Spatial and Planar Parallel Manipulators With Prismatic Actuators

1998 ◽  
Author(s):  
Marc Leblond ◽  
Clément M. Gosselin
Keyword(s):  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Static Balancing ◽  
Inertial Parameters ◽  
Dimensional Parameters ◽  
Balancing Conditions ◽  
Static Conditions ◽  
Planar Parallel Manipulators

Abstract In this paper, the static balancing of existing spatial and planar parallel manipulators by the addition of balancing elements is addressed. Static balancing is defined here as the set of conditions on manipulator dimensional and inertial parameters which, when satisfied, ensure that the weight of the links does not produce any force (or torque) at the actuators for any configuration of the manipulator, under static conditions. These conditions are derived here for spatial six-degree-of-freedom parallel manipulators and it is shown that planar three-degree-of-freedom parallel manipulators can be treated as a particular case of the spatial 6-dof mechanisms. The static balancing conditions associated with planar mechanisms can therefore easily be found, but are not given here because of space limitations. A brief geometric interpretation of the balancing conditions which are associated with statically balanced spatial mechanisms is then carried out. It is shown that balancing is generally possible even when the dimensional parameters are imposed, which is a useful property since dimensional parameters are usually obtained from kinematic design or optimization. Finally, examples of balanced planar and spatial parallel manipulators are given. Static balancing leads to considerable reduction in the actuator forces (or torques), which in turn leads to less powerful actuators and more efficient designs. Moreover, the possibility of balancing existing systems by introducing additional elements, as demonstrated here, is of interest for retrofitting existing parallel mechanisms.

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