FLEXURE HINGE OR ELASTIC HINGE

Construction fundamentals

INTRODUCTION

A JPE Precision Point sheet about the formulas of flexure hinge design and flexure hinge stiffness to benefit your play free and frictionless system design. Rules of thumb for manufacturability versus hinge functionality. Also, different  configurations are provide with their own benefits.

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Stiffness at point A

D=\frac{2d_1d_2}{d_1+d_2} , D(d_2={\infty})=2d_1 (straight, see below)
C_{Ax}=0.48Et\sqrt{\frac {h}{D}
C_{A_y}^{\ast }>\frac{GA}{l}=\frac{Ght}{D}=\frac{Eht}{2D(1+\nu )}

* No acknowledged equation. Above stated equation can only be used as a rough estimate

C_{Az}=0.56Et\sqrt{\frac{h}{D}} (\frac{1}{1.2+\frac{D}{h}})
K_{Ax}=\frac {1}{12}t^2\ast C_z=0.047Et^3\sqrt{\frac {h}{D}}(\frac {1}{1.2+\frac {D}{h}})
K_{Ay}=0.093Eth^2\sqrt{\frac {h}{D}}
K_{Az}=\frac {1}{12}t^2\ast C_x=0.04Et^3\sqrt{\frac {h}{D}}

Stiffness at point B

C_{Bx}=C_{Ax}

\frac {1}{C_{By}}=\frac {1}{C_{Ay}}+\frac{L^2}{K_{Az}}

C_{BY}=\frac{C_{Ay}K_{Az}}{K_{Az}+C_{Ay}L^2}

\frac {1}{C_{Bz}}=\frac {1}{C_{Az}}+\frac{L^2}{K_{Ay}}

C_{BZ}=\frac{C_{Az}K_{Ay}}{K_{Ay}+C_{Az}L^2}

Other properties

u_z=\frac{F_z}{C_{Bz}}
R_y=\frac{F_zL}{K_{Ay}}
\sigma _{max}{\approx}0.58E\sqrt{\frac{h}{D}}\ast R_y=ES\ast R_y

Version with equal h, Cx and Ky
FLEXURE HINGE OR ELASTIC HINGE with equal h C_x and K_y
FLEXURE HINGE OR ELASTIC HINGE with equal h C_x and K_y 02
Elastic hinge
Design rules of thumb

Elastic hinge parameter:  \beta =\frac {h}{D}

  • Realistic area: 0.01 < \beta <0.5
  • \beta < 0.01: manufacturability
  • \beta > 0.5: hinge functionality gone

Trade-off between:

  • Maximum C_{Ax}: \beta =0.5
  • Minimum K_{Ay}: \beta =0.01

Normalized:

  • C_{Ax \ norm}=0.48\sqrt{\beta }
  • K_{Ay \ norm}=1.3\sqrt{\beta }-0.42\beta -0.034\beta ^{1.5}
  • S=0.58\sqrt{\beta }
Design rules of thumb

Source:
• Constructieprincipes, voor het nauwkeurig bewegen en positioneren, M.P. Koster. ISBN 978-90-5574-610-1

This page uses QuickLaTeX to display formulas.