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Research Papers

Negative Stiffness Building Blocks for Statically Balanced Compliant Mechanisms: Design and Testing

[+] Author and Article Information
Karin Hoetmer, Just Herder

Department of Biomechanical Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands

Geoffrey Woo, Charles Kim

Department of Mechanical Engineering, Bucknell University, Lewisburg, PA 17837

J. Mechanisms Robotics 2(4), 041007 (Sep 30, 2010) (7 pages) doi:10.1115/1.4002247 History: Received August 29, 2009; Revised July 13, 2010; Published September 30, 2010; Online September 30, 2010

In some applications, nonconstant energy storage in the flexible segments of compliant mechanisms is undesired, particularly when high efficiency or high-fidelity force feedback is required. In these cases, the principle of static balancing can be applied, where a balancing segment with a negative stiffness is added to cancel the positive stiffness of the compliant mechanism. This paper presents a strategy for the design of statically balanced compliant mechanisms and validates it through the fabrication and testing of proof-of-concept prototypes. Three compliant mechanisms are statically balanced by the use of compressed plate springs. All three balanced mechanisms have approximately zero stiffness but suffer from a noticeable hysteresis loop and finite offset from zero force. Design considerations are given for the design and fabrication of statically balanced compliant mechanisms.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Statically balanced rigid mechanisms (1)

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Figure 2

Rigid body model of a preloaded compression spring in different positions with the potential energy (V), the force in horizontal direction (Fu), and the stiffness (K) throughout the range of motion. (a) The initial position (unstable equilibrium), the spring is fully preloaded; (b) the mechanism is exhibiting negative stiffness; (c) the turning point from negative to positive stiffness; (d) the mechanism is fully relaxed (stable equilibrium); (e) the spring is extended.

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Figure 3

Balancing building blocks: (a) compressed leaf spring (8), (b) compressed leaf spring with tensural pivots (9), and (c) compressed plate spring (10). The arrows indicate the location and direction of the generated force (F) and displacement (u).

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Figure 4

(a) Plate spring (10) with length 2L and (b) plate spring compressed at both ends with preload displacement dL and constrained in vertical direction in the middle of the beam. The location and direction of the generated force (F) and displacement (u) are indicated by the arrow.

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Figure 5

Force-displacement behavior of the plate spring element. The first part (before umax) indicates the approximately linear part.

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Figure 6

Three compliant mechanisms. From left to right: gripper configuration 1, gripper configuration 2, and multiplier.

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Figure 7

Experimental set-up with gripper configuration 1

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Figure 8

Force-displacement data of gripper configuration 1 with and without balancers

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Figure 9

Force-displacement data of gripper configuration 2 with and without balancers

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Figure 10

Force-displacement data of the multiplier with and without balancers

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Figure 11

Force-displacement data of the slider without any application attached shows the hysteresis in the slider

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Figure 12

(a) Force-displacement data of balancers of Delrin on the linear slide. The different cycles show different stiffnesses with the first cycle and the last cycle. The balancers lose stiffness over time, which indicates stress relaxation. (b) Force-displacement data of spring steel balancers on the linear slide. The different cycles show the same stiffness, which indicates that there is no stress relaxation.

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