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Research Papers

Design of a Linear Bistable Compliant Crank–Slider Mechanism

[+] Author and Article Information
Ahmad Alqasimi

Department of Mechanical Engineering,
University of South Florida,
4202 East Fowler Avenue,
ENB 118,
Tampa, FL 33620
e-mail: aalqasim@mail.usf.edu

Craig Lusk

Associate Professor
Department of Mechanical Engineering,
University of South Florida,
4202 East Fowler Avenue,
ENB 118,
Tampa, FL 33620
e-mail: clusk2@eng.usf.edu

Jairo Chimento

Department of Mechanical Engineering,
University of South Florida,
4202 East Fowler Avenue,
ENB 118,
Tampa, FL 33620
e-mail: Jairo.chimento@gmail.com

Manuscript received September 14, 2015; final manuscript received January 6, 2016; published online May 4, 2016. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 8(5), 051009 (May 04, 2016) (15 pages) Paper No: JMR-15-1264; doi: 10.1115/1.4032509 History: Received September 14, 2015; Revised January 06, 2016

This paper presents a new model for a linear bistable compliant mechanism and design guidelines for its use. The mechanism is based on the crank–slider mechanism. This model takes into account the first mode of buckling and postbuckling behavior of a compliant segment to describe the mechanism's bistable behavior. The kinetic and kinematic equations, derived from the pseudo-rigid-body model (PRBM), were solved numerically and are represented in plots. This representation allows the generation of step-by-step design guidelines. The design parameters consist of maximum desired deflection, material selection, safety factor, compliant segments' widths, maximum force required for actuator selection, and maximum footprint (i.e., the maximum rectangular area that the mechanism can fit inside of and move freely without interfering with other components). Because different applications may have different input requirements, this paper describes two different design approaches with different parameters subsets as inputs. The linear bistable compliant crank–slider mechanism (LBCCSM) can be used in the shape-morphing space-frame (SMSF) as potential application. The frame's initial shape is constructed from a single-layer grid of flexures, rigid links, and LBCCSMs. The grid is bent into the space-frame's initial cylindrical shape, which can morph because of the inclusion of LBCCSMs in its structure.

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References

Figures

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Fig. 1

The mechanism considered, point A is fixed where point B and C are living hinges

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Fig. 2

Adapted from Ref. [1]. (a) An elastic fixed-pinned cantilever beam and (b) its PRBM.

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Fig. 3

Adapted from Ref. [1]. (a) An elastic pinned–pinned cantilever beam and (b) its PRBM.

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Fig. 4

The LBCCSM model: (a) segment 2 does not buckle in the first case and (b) the axial load in segment 2 is sufficient to buckle it in the second case

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Fig. 5

LBCCSM model at (a) initial state and (b) intermediate state

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Fig. 6

Internal force analysis

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Fig. 9

The nondimensional force (f) with respect to the second segment's initial angle (θ2i) over range of stiffness coefficient ratio (v) for (a) θ1 = 30 deg, (b) θ1 = 50 deg, and (c) θ1 = 70 deg

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Fig. 10

The nondimensional coefficient (J) with respect to the second segment's initial angle (θ2i) for θ1 = 30 deg over range of stiffness coefficient ratio (v). Part (a) for lower force range and part (b) for higher force range.

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Fig. 8

The first segment's PRBM angle (Θ1) with respect to the second segment's initial angle (θ2i) over range of stiffness coefficient ratio (v) for (a) θ1 = 30 deg, (b) θ1 = 50 deg, and (c) θ1 = 70 deg

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Fig. 7

The footprint (bmax/X) with respect to the second segment's initial angle (θ2i) over range of stiffness coefficient ratio (v) for (a) θ1 = 30 deg, (b) θ1 = 50 deg, and (c) θ1 = 70 deg

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Fig. 11

The nondimensional coefficient (J) with respect to the second segment's initial angle (θ2i) for θ1 = 50 deg over range of stiffness coefficient ratio (v). Part (a) for lower force range and part (b) for higher force range.

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Fig. 12

The nondimensional coefficient (J) with respect to the second segment's initial angle (θ2i) for θ1 = 70 deg over range of stiffness coefficient ratio (v). Part (a) for lower force range and part (b) for higher force range.

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Fig. 13

The design flow chart for the first approach

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Fig. 14

The design flow chart for the second approach

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Fig. 15

Example 1: force–displacment and work–displacment curves

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Fig. 23

Spherical SMSF using matlab. Initial state (left) and final state (right).

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Fig. 24

The single-layer grid tessellation showing the LBCCSM placement for the spherical SMSF

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Fig. 25

The spherical SMSF before morphing showing the grid being bent to space-frame's initial cylindrical shape

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Fig. 26

The spherical SMSF after applying CCW torque loading

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Fig. 27

The spherical SMSF after applying vertical loading

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Fig. 16

Example 2: force–displacment and work–displacment curves

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Fig. 17

LBCCSM elements showing the two stable positions: (a) open and (b) closed

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Fig. 18

Hyperbolic SMSF using matlab. Initial state (left) and final state (right).

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Fig. 19

The single-layer grid tessellation showing the LBCCSM placement for the hyperbolic SMSF

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Fig. 20

The hyperbolic SMSF before morphing showing the grid being bent to space-frame's initial cylindrical shape

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Fig. 21

The hyperbolic SMSF after applying CW torque loading

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Fig. 22

The hyperbolic SMSF after applying radial loading

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