Skip to Main Content
Table 3.

Calculation of the maximum bending stress of the claw

TermEquationsExocuticleExocuticle+endocuticleUnits
D  129.35  μm
d  94.55 39.47 μm
B  129.35  μm
b  17.38 44.92 μm
H  125.1  μm
h  12.39 39.93 μm
IA
$$I_{\mathrm{A}}=0.00686(D^{4}-d^{4})-\frac{0.0177D^{2}d^{2}(D-d)}{(D+d)}$$

960667.09 1658113.70 μm4
YA
$$Y_{\mathrm{A}}=\frac{2}{3{\pi}}\frac{D^{2}+Dd+d^{2}}{D+d}$$

35.92 29.41 μm
IB
$$I_{\mathrm{B}}=\frac{Bh^{3}+2b(H-h)^{3}}{12}+Bh\left(Y_{\mathrm{B}}-\frac{h}{2}\right)^{2}+2b(H-h)\left(\frac{H-h}{2}+h-Y_{\mathrm{B}}\right)^{2}$$

8618001.24 59474144.34 μm4
YB
$$Y_{\mathrm{B}}=\frac{Bh^{2}+2b(H^{2}-h^{2})}{2[Bh+2b(H-h)]}$$

50.586 114.62 μm
SA
$$S_{\mathrm{A}}=\frac{{\pi}}{8}(D^{2}-d^{2})$$

3059.8 5958.64 μm2
SB
$$S_{\mathrm{B}}=2b(H-h)+Bh$$

5520.45 12816.62 μm2
IT
$$I_{\mathrm{T}}=I_{\mathrm{A}}+S_{\mathrm{A}}(Y_{\mathrm{A}}+Y_{\mathrm{T}})^{2}+I_{\mathrm{B}}+S_{\mathrm{B}}(H-Y_{\mathrm{B}}-Y_{\mathrm{T}})^{2}$$

10013484.52 67604619.72 μm4
Critical
$$\frac{{\delta}I_{\mathrm{T}}}{{\delta}Y}=2S_{\mathrm{A}}(Y_{\mathrm{A}}+Y_{\mathrm{T}})+2S_{\mathrm{B}}(H-Y_{\mathrm{B}}-Y_{\mathrm{T}})(-1)=0$$

YT
$$Y_{\mathrm{T}}=\frac{S_{\mathrm{B}}(H-Y_{\mathrm{B}})-S_{\mathrm{A}}Y_{\mathrm{A}}}{S_{\mathrm{A}}+S_{\mathrm{B}}}$$

35.13 -2.177 μm
Ymax
$$Y_{\mathrm{max}}=H-Y_{\mathrm{T}}$$

89.97 127.277 μm
σmax
$${\sigma}_{\mathrm{max}}=\frac{M}{I_{\mathrm{max}}}Y_{\mathrm{max}}$$

684.2 143.4 N mm-2
TermEquationsExocuticleExocuticle+endocuticleUnits
D  129.35  μm
d  94.55 39.47 μm
B  129.35  μm
b  17.38 44.92 μm
H  125.1  μm
h  12.39 39.93 μm
IA
$$I_{\mathrm{A}}=0.00686(D^{4}-d^{4})-\frac{0.0177D^{2}d^{2}(D-d)}{(D+d)}$$

960667.09 1658113.70 μm4
YA
$$Y_{\mathrm{A}}=\frac{2}{3{\pi}}\frac{D^{2}+Dd+d^{2}}{D+d}$$

35.92 29.41 μm
IB
$$I_{\mathrm{B}}=\frac{Bh^{3}+2b(H-h)^{3}}{12}+Bh\left(Y_{\mathrm{B}}-\frac{h}{2}\right)^{2}+2b(H-h)\left(\frac{H-h}{2}+h-Y_{\mathrm{B}}\right)^{2}$$

8618001.24 59474144.34 μm4
YB
$$Y_{\mathrm{B}}=\frac{Bh^{2}+2b(H^{2}-h^{2})}{2[Bh+2b(H-h)]}$$

50.586 114.62 μm
SA
$$S_{\mathrm{A}}=\frac{{\pi}}{8}(D^{2}-d^{2})$$

3059.8 5958.64 μm2
SB
$$S_{\mathrm{B}}=2b(H-h)+Bh$$

5520.45 12816.62 μm2
IT
$$I_{\mathrm{T}}=I_{\mathrm{A}}+S_{\mathrm{A}}(Y_{\mathrm{A}}+Y_{\mathrm{T}})^{2}+I_{\mathrm{B}}+S_{\mathrm{B}}(H-Y_{\mathrm{B}}-Y_{\mathrm{T}})^{2}$$

10013484.52 67604619.72 μm4
Critical
$$\frac{{\delta}I_{\mathrm{T}}}{{\delta}Y}=2S_{\mathrm{A}}(Y_{\mathrm{A}}+Y_{\mathrm{T}})+2S_{\mathrm{B}}(H-Y_{\mathrm{B}}-Y_{\mathrm{T}})(-1)=0$$

YT
$$Y_{\mathrm{T}}=\frac{S_{\mathrm{B}}(H-Y_{\mathrm{B}})-S_{\mathrm{A}}Y_{\mathrm{A}}}{S_{\mathrm{A}}+S_{\mathrm{B}}}$$

35.13 -2.177 μm
Ymax
$$Y_{\mathrm{max}}=H-Y_{\mathrm{T}}$$

89.97 127.277 μm
σmax
$${\sigma}_{\mathrm{max}}=\frac{M}{I_{\mathrm{max}}}Y_{\mathrm{max}}$$

684.2 143.4 N mm-2
Close Modal