0
Research Papers

An Energy Approach to Static Balancing of Systems With Torsion Stiffness

[+] Author and Article Information
Giuseppe Radaelli1

 InteSpring B.V., Molengraaffsingel 12, Delft 2629 JD, The Netherlandsgiuseppe@intespring.nl

Juan A. Gallego

 Department of BioMechanical Engineering, 3ME – BmechE, Delft University of Technology, Delft 2628 CD, The Netherlandsj.a.gallegosanchez@tudelft.nl

Just L. Herder

 Department of BioMechanical Engineering, 3ME – BmechE, Delft University of Technology, Delft 2628 CD, The Netherlandsj.l.herder@tudelft.nl

1

Corresponding author.

J. Mech. Des 133(9), 091006 (Sep 15, 2011) (8 pages) doi:10.1115/1.4004704 History: Received December 09, 2010; Revised July 19, 2011; Accepted July 22, 2011; Published September 15, 2011; Online September 15, 2011

Static balance can be applied to improve the energy efficiency of mechanisms. In the field of static balancing, there is a lack of knowledge and design methods that are capable of dealing with torsional stiffness. This paper presents a design approach for statically balanced mechanisms, with the focus on mechanisms with torsional stiffness. The approach is graphical in nature and is based on the requirement of constant potential energy. The first achievements of this approach are presented as two conceptual designs of different types of mechanisms. One of them is developed further into a prototype and tested. The prototype has a correlation coefficient of 0.96 and a normalized mean squared error of 0.12 with respect to the mechanical model of the conceptual design.

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Step diagram: Outline of the presented design approach. After the evaluation it is possible to go back to the previous steps if the results are not satisfactory.

Grahic Jump Location
Figure 2

First basic element: Single link with a torsion spring, (a) Model, (b) Potential energy with k = 1, l = 1 and φ0  = 0.5 rad. Range from − 4π to 4π.

Grahic Jump Location
Figure 3

Second basic element: Dyad consisting of two links and two torsion springs. Two configurations are possible for a given point C, namely elbow-up and elbow-down.

Grahic Jump Location
Figure 4

The potential energy of a dyad is a linear combination of the energy in both springs. (a) The contribution of the first spring, kB  = 0, φa=-π4. (b) The contribution of the second spring, kA  = 0, φb=π2. (c) Linear combination of two springs, elbow-down.

Grahic Jump Location
Figure 5

Potential energy of two dyads joined at point P. (a) One elbow-up and one elbow-down, (b) both elbow-down, (c) both elbow-up, and (d) one elbow-down and one elbow-up.

Grahic Jump Location
Figure 6

(a) Model of Example 1. (b) Potential energy graph. (c) Potential energy over constrained path. (d) Force over constrained path. The dashed-red and dotted-green lines are the separate dyads and the continuous-blue line is the coupled system.

Grahic Jump Location
Figure 7

(a) Model of Example 2. (b) Potential energy graph. (c) Potential energy along the bottom path where x = 0. (d) Force along the bottom path where x = 0. The dashed-red and dotted-green lines are half systems and the continuous-blue line is the coupled system.

Grahic Jump Location
Figure 8

Prototype model results. (a) The potential energy along the constrain line and (b) force along constrain line. The dashed-red and dotted-green lines are the separate dyads and the continuous-blue line is the coupled system.

Grahic Jump Location
Figure 9

Picture of the modular prototype

Grahic Jump Location
Figure 10

Test setup schematic. A = mechanism, B = tensile force tester, C = pulley, D = mass, E = string, F = constraining rail.

Grahic Jump Location
Figure 11

Measurement results. (a) For every set of three lines from top to bottom: Forward measurement, mean of forward and backward, backward measurement. Measurements are preformed on the Mechanism with the Setup and on the Setup separately, the difference of both gives the values for the Mechanism alone. (b) Mean force of Mechanism alone (Fig. 1a) compared with modeled force (Fig. 8b).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In