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Research Papers: Design of Mechanisms and Robotic Systems

Experimental Characterization of a T-Shaped Programmable Multistable Mechanism

[+] Author and Article Information
Mohamed Zanaty

Instant-Lab
Ecole Polytechnique Fédérale de Lausanne (EPFL),
Neuchâtel 2000, Switzerland
e-mail: mohamed.zanaty@epfl.ch

Simon Henein

Instant-Lab
Ecole Polytechnique Fédérale de Lausanne (EPFL),
Neuchâtel 2000, Switzerland
e-mail: simon.henein@epfl.ch

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 4, 2018; final manuscript received April 6, 2018; published online June 8, 2018. Assoc. Editor: Massimo Callegari.

J. Mech. Des 140(9), 092301 (Jun 08, 2018) (10 pages) Paper No: MD-18-1005; doi: 10.1115/1.4040173 History: Received January 04, 2018; Revised April 06, 2018

Programmable multistable mechanisms (PMM) exhibit a modifiable stability behavior in which the number of stable states, stiffness, and reaction force characteristics are controlled via their programming inputs. In this paper, we present experimental characterization for the concept of stability programing introduced in our previous work (Zanaty et al., 2018, “Programmable Multistable Mechanisms: Synthesis and Modeling,” ASME J. Mech. Des., 140(4), p. 042301.) A prototype of the T-combined axially loaded double parallelogram mechanisms (DPM) with rectangular hinges is manufactured using electrodischarge machining (EDM). An analytical model based on Euler–Bernoulli equations of the T-mechanism is derived from which the stability behavior is extracted. Numerical simulations and experimental measurements are conducted on programming the mechanism as monostable, bistable, tristable, and quadrastable, and show good agreement with our analytical derivations within 10%.

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Figures

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Fig. 1

Two degree of programing T-combined DPM composed of (a) distributed stiffness blades and (b) lumped stiffness rectangular hinges

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Fig. 4

(a) T-mechanism monolithically manufactured by EDM, (b) schematic representation of the measurement setup, and (c) realization of the measurement setup

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Fig. 3

Equivalent rigid body diagram of the T-mechanism

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Fig. 2

(a) T-mechanism, (b) key dimensions, and (c) forces and displacements

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Fig. 5

Stable state q0 of the mechanism programmed in monostable region based on FEM (left) and experiment (right)

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Fig. 6

The reaction force of the mechanism when programmed as monostable for p1=0.0 (mm) and p2=0.0 (mm)

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Fig. 7

Stable states, q1± and unstable state, q0 of the mechanism programmed in bistable region I based on FEM (top) and experiment (bottom)

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Fig. 8

The reaction force of the mechanism programmed as bistable in region I for p1=−0.15 (mm), p2=1.1 (mm)

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Fig. 9

Stable states, q3± and unstable state, q0 of the mechanism programmed in bistable region II based on FEM (top) and experiment (bottom)

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Fig. 10

The reaction force of the mechanism programmed as bistable in region II for p1=0.39 (mm), p2=−0.9 (mm)

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Fig. 11

Stable states, q0, q3± and unstable states, q2± of the mechanism programmed in tristable region based on FEM (top) and experiment (bottom)

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Fig. 12

The reaction force of the mechanism programmed as tristable for p1=0.37 (mm), p2=0.0 (mm)

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Fig. 15

Programming diagram of the T-mechanism in which stability boundaries p1cr, p2a, p2b, p2c are experimentally verified

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Fig. 13

Stable states, q1±, q3±, and unstable states, q0, q2± of the mechanism programmed in quadrastable region based on FEM (top) and experiment (bottom)

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Fig. 14

The reaction force of the mechanism programmed as quadrastable for p1=0.36 (mm), p2=2.8 (mm). The inset illustrates the reaction force upon switching between second and third stable states.

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Fig. 17

(a) Selected p2 values of the calculated equilibrium position diagrams as p1 varies from −0.2 (mm) to 0.5 (mm). Equilibrium positions diagram at (b) p2=−1 (mm), (c)p2=0 (mm), (d) p2=1 (mm), and (e) p2=3 (mm) verified numerically and experimentally.

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Fig. 16

(a) Selected p1 values of the calculated equilibrium position diagrams as p2 varies from −4 (mm) to 4 (mm), equilibrium positions diagram at (b) p1=−0.1 (mm), and (c) p1=0.35 (mm) verified both numerically and experimentally

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