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Research Papers

Design of a Compact Gravity Equilibrator With an Unlimited Range of Motion

[+] Author and Article Information
Bob G. Bijlsma

Faculty of Mechanical, Maritime and
Materials Engineering,
Delft University of Technology,
Delft 2628 CA, The Netherlands;
InteSpring B.V.,
Delft 2629 JD, The Netherlands

Giuseppe Radaelli

Faculty of Mechanical, Maritime and
Materials Engineering,
Delft University of Technology,
Delft 2628 CA, The Netherlands;
InteSpring B.V.,
Delft 2629 JD, The Netherlands
e-mails: g.radaelli@tudelft.nl;
giuseppe@intespring.nl

Just L. Herder

Faculty of Mechanical, Maritime and
Materials Engineering,
Delft University of Technology,
Delft 2628 CA, The Netherlands
e-mail: j.l.herder@tudelft.nl

Manuscript received September 2, 2016; final manuscript received July 28, 2017; published online September 18, 2017. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 9(6), 061003 (Sep 18, 2017) (9 pages) Paper No: JMR-16-1260; doi: 10.1115/1.4037616 History: Received September 02, 2016; Revised July 28, 2017

A gravity equilibrator is a statically balanced system which is designed to counterbalance a mass such that any preferred position is eliminated and thereby the required operating effort to move the mass is greatly reduced. Current spring-to-mass gravity equilibrators are limited in their range of motion as a result of constructional limitations. An increment of the range of motion is desired to expand the field of applications. The goal of this paper is to present a compact one degree-of-freedom mechanical gravity equilibrator that can statically balance a rotating pendulum over an unlimited range of motion. Static balance over an unlimited range of motion is achieved by a coaxial gear train that uses noncircular gears. These gears convert the continuous rotation of the pendulum into a reciprocating rotation of the torsion bars. The pitch curves of the noncircular gears are specifically designed to balance a rotating pendulum. The gear train design and the method to calculate the parameters and the pitch curves of the noncircular gears are presented. A prototype is designed and built to validate that the presented method can balance a pendulum over an unlimited range of motion. Experimental results show a work reduction of 87% compared to an unbalanced pendulum and the hysteresis in the mechanism is 36%.

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Figures

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Fig. 1

An exploded view of the different components to distinguish the parameters of the gravity equilibrator. On the left, a torsion spring of which the angle of rotation is defined by θout, and on the right, a rotating mass on an arm, that is, defined by the angle θin.

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Fig. 2

The relation between θin and θout to obtain a statically balanced system. For increasing θin, θout first increases and then decreases again.

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Fig. 3

A schematic representation of the gear train: (a) a three-dimensional representation of the gear train to visualize the topology, (b) the first gear set which consists of two circular gears, and (c) the second gear set which consists of two noncircular gears, visualized by oval gears

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Fig. 4

The four possible variations based on the original concept: (a) the original concept where all four gears have external toothing, (b) the concept where gear 1 is replaced by a gear with internal toothing, (c) the concept where gear 4 is replaced by a gear with internal toothing, and (d) the concept where both gear 1 and 4 are replaced by gears with internal toothing

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Fig. 5

The pitch curves of (a) gear set #1 and (b) gear set #2. (a) The outer gear (black) is gear 1, the inner gear (yellow) is gear 2. (b) The inner gear (red) is gear 3 and the outer gear (blue) is gear 4. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

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Fig. 6

A visualization of the positions of the gears at different moments. These moments are referred to in (a): (a) the graph where the angle θin and θout are plotted, (b) the initial position where θin and θout are zero, (c) and (d) other moments where both θin and θout are increasing, (e) at this moment θout is maximal, (f) a moment where θin increases and θout decreases, and (g) the initial position which is equal to (b).

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Fig. 7

The pitch curves of the four gears with the teeth: (a) the pitch curve of gear 1 and the internal teeth, (b) the pitch curve of gear 2 and the external teeth, (c) the pitch curve of gear 3 and the external teeth, and (d) the pitch curve of gear 4 and the internal teeth

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Fig. 8

Pictures of the prototype: (a) a general overview, (b) fixed internal gear 1, (c) gear 2 and gear 3 combined, (d) output gear 4, and (e) the structure that connects the multiple parts

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Fig. 9

A schematic overview of the measurement setup. A pulley is attached to the pendulum. Two different cables are attached to this pulley. One of these cables is connected to the testing machine and one cable is connected to a counterweight of 5 kg.

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Fig. 10

The measurement results of three consecutive measurements from 0 to 4π rad and back. The hysteresis loop is shown (red) together with the mean value of the hysteresis loop (black). Also, the mean value of the moment exerted by the unbalanced pendulum (green) is shown for reference. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

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Fig. 11

The hysteresis in the gear transmission which is not loaded by the torsion bars. Only the counterweight is added to the mechanism for the measurements. The hysteresis in the unloaded system is around 0.

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Fig. 12

Angle θout changes discontinuously when the pendulum is in the upright position. This results in a jump in the pitch curves of the noncircular gears 3 and 4. This discontinuity is caused by the required energy that the spring has to absorb to achieve perfect balance.

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Fig. 13

The pitch curves when the angle θout can also become negative. It is seen that the pitch curves of gear 3 (red) and gear 4 (blue) are now continuous but have multiple loops. This configuration of gears is impossible without having intersecting gears. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

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