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Research Papers

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

[+] Author and Article Information
Rogier Barents, Mark Schenk, Wouter D. van Dorsser

Boudewijn M. Wisse

Inte Spring B.V., Rotterdamseweg 145, 2628 AL Delft, The NetherlandsBoudewijn@InteSpring.nl

Just L. Herder1

Department of Biomechanical Engineering,  Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands e-mail: J.L.Herder@TUDelft.nl

1

Corresponding author.

J. Mech. Des 133(6), 061010 (Jun 21, 2011) (10 pages) doi:10.1115/1.4004101 History: Received December 24, 2009; Revised September 14, 2010; Published June 21, 2011; Online June 21, 2011

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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Basic gravity equilibrator using a zero-free-length spring balancing a mass m with lengths a, r, L, which satisfies the balancing condition (4) for any angle ϕ

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Figure 2

A basic gravity equilibrator using a zero-free-length spring (a) can be replaced by a conventional spring using a wire and pulley (b) but it will be a nonexact solution as the wrap angle β will depend on the position of the weight arm (ϕ). This can be resolved by employing a three-pulley solution (c) and (d) where the total length of wire wrapped around the pulleys will always be constant (sum of wrap angles βi is constant) and the solution will therefore be exact.

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Figure 3

Schematic representation of the energy-free adjustment process of the basic gravity equilibrator (a). When balancing the mass, energy is exchanged between the mass and the balancer spring, and the energy in the storage spring (Ustorage ) is kept constant (b). Subsequently, the mass is locked. (c) During adjustment, the potential energy of the mass is kept constant, and energy is exchanged between the storage spring and balancer spring until it has been adjusted to correspond with the potential energy of the new mass (d). After adjustment, the energy in the storage spring is kept constant, while energy is again exchanged between mass and balancer spring.

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Figure 4

(a) The basic spring-to-spring balancer using zero-free-length springs is in equilibrium for any configuration of the bar (ϕ) provided the spring and bar attachment points are collinear and the following condition is met: a1k1r1=a2k2r2. The balancer can easily be adapted to using conventional springs with either a nonexact or (b) an exact solution (c).

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Figure 5

The balanced bar spring-to-spring balancer, (a) as a simple modification of the basic spring-to-spring balancer, where the fixed pivot point of the bar and springs are placed along a vertical and a1k1r=a2k2r must be satisfied. Again this balancer can easily be adapted to using conventional springs with nonexact and exact solutions, for instance, according to (b) and (c), respectively.

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Figure 6

The “sliding ladder” spring-to-spring balancer with two equal zero-free-length springs (a) merely requires the two sliding surfaces to be perpendicular to each other. Extending the balancer to using conventional springs is trivial by storing the rest length behind the sliding surfaces (b). A variant with the two springs vertical and parallel is shown in (c). Note that no three-pulley mechanisms are required as the wrap angle around the pulleys is constant at all times.

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Figure 7

The parallelogram spring-to-spring balancer; (b) can be considered as being constructed from four “sliding ladder” balancers; (a) adapted from Ref. 1. It is in equilibrium for any position of its bars. The vertical spring is replaced by a conventional spring by storing its rest length outside the parallelogram. Other practical embodiments may include a combination of extension and compression springs, indicated by E and C, respectively. In (c), a compression spring is used in combination with a conventional extension spring by storing its rest length inside the parallelogram. In (d), three compression springs counterbalance each other. In (e), one compression spring balances two zero-free-length extension springs.

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Figure 8

The parallelogram spring-to-spring balancer employed as storage spring for the gravity equilibrator (using zero-free-length springs). In the horizontal position the weight arm is locked and the height of the parallelogram can be changed in an energy-free way (a). Once adapted to the new weight (b), the top end of the parallelogram is fixed and the system is again statically balanced for any ϕ.

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Figure 9

The rolling link spring-to-spring balancer (a) consists of a bar rolling on a support disk, with two fixed pulleys on either end. The wires connected to the springs run over the fixed disks at the end of the rolling bar. As shown in (b) the system works by creating two isosceles triangles having one side with length L/2 lying back to back. In order for the wires to be parallel to the isosceles triangles (c) the radius of the rolling links rr must be equal to rp2 . In (d) the wrap angles of the wire are determined, and it is shown that Σβi=π/2, independent of ϕ. Therefore, the balancing is exact.

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Figure 10

Practical implementation of a gravity equilibrator using the parallelogram storage spring principle with zero-free-length spring as shown in Fig. 8. In the configuration shown the parallelogram is locked (black knob). When the weight arm is in horizontal position, it can be locked, in which case the parallelogram can be unlocked and moved upward (for a greater payload) or downward (for smaller payload).

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Figure 11

Practical implementation of rolling link adjustment mechanism in a kitchen cabinet. The kitchen cabinet moves in a 90 degree arc by means of a parallelogram, and its mass is balanced by a three-pulley basic gravity equilibrator attached to the bottom arm. When the cabinet is in its lowest position, it is fixed and the rolling link spring-to-spring balancer is unlocked. Mass can be added to or removed from the cabinet, and the balancer spring is adjusted accordingly by means of the rolling link balancer.

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Figure 12

The actual embodiment of the practical implementation of rolling link adjustment mechanism in a kitchen cabinet. The schematic representation is given in Fig. 1.

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Figure 13

The rolling link spring-to-spring balancing mechanism (a) as implemented in the balanced kitchen cabinet. Two parallel support disks are used, to allow the wires to pass through the centre. In (b) and (c), the actual embodiment is shown. The schematic representation is given in Fig. 9.

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Figure 14

Solution to balance the mass of the rolling link. Assuming that the centre of mass of the rolling bar coincides with the centre of the rolling link, the mass can be balanced by means of a zero-free-length spring. Essentially it is a rolling link variant of the basic gravity equilibrator, and the dimensions are equivalent to the ones shown in Fig. 1. Distance a may of course be greater than the radius of the fixed disk.

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