A biomechanical model of the lumbar region of the human trunk is shown. The forces acting in the four muscle groups consist of ${ F }_{ R }$ for the rectus, ${ F }_{ O }$ for the oblique, ${ F }_{ L }$ for the lumbar latissimus dorsi, and ${ F }_{ E }$ for the erector spinae. These loadings are symmetric with respect to the $y - z$ plane. Replace this system of parallel forces by an equivalent force and couple moment acting at the spine, point $O$ . Express the results in Cartesian vector form.

Given:

${ F }_{ R }$ = $35$ $N\quad a$ = $75$ $mm$

${ F }_{ O }$ = $45$ $N\quad b$ = $45$ $mm$

${ F }_{ L }$ = $23$ $N\quad c$ = $15$ $mm$

${ F }_{ E }$ = $32$ $N\quad d$ = $50$ $mm$

$e$ = $40$ $mm\quad f$ = $30$ $mm$

Question

A biomechanical model of the lumbar region of the human trunk is shown. The forces acting in the four muscle groups consist of ${ F }_{ R }$ for the rectus, ${ F }_{ O }$ for the oblique, ${ F }_{ L }$ for the lumbar latissimus dorsi, and ${ F }_{ E }$ for the erector spinae. These loadings are symmetric with respect to the $y - z$ plane. Replace this system of parallel forces by an equivalent force and couple moment acting at the spine, point $O$ . Express the results in Cartesian vector form.

Given:

${ F }_{ R }$ = $35$ $N\quad a$ = $75$ $mm$

${ F }_{ O }$ = $45$ $N\quad b$ = $45$ $mm$

${ F }_{ L }$ = $23$ $N\quad c$ = $15$ $mm$

${ F }_{ E }$ = $32$ $N\quad d$ = $50$ $mm$

$e$ = $40$ $mm\quad f$ = $30$ $mm$

Given:

[latex]{ F }_{ R }[/latex] = [latex]35[/latex] [latex]N\quad a[/latex] = [latex]75[/latex] [latex]mm[/latex]

[latex]{ F }_{ O }[/latex] = [latex]45[/latex] [latex]N\quad b[/latex] = [latex]45[/latex] [latex]mm[/latex]

[latex]{ F }_{ L }[/latex] = [latex]23[/latex] [latex]N\quad c[/latex] = [latex]15[/latex] [latex]mm [/latex]

[latex]{ F }_{ E }[/latex] = [latex]32[/latex] [latex]N\quad d[/latex] = [latex]50[/latex] [latex]mm[/latex]

[latex]e[/latex] = [latex]40[/latex] [latex]mm\quad f[/latex] = [latex]30[/latex] [latex]mm[/latex]

Accepted Answer

[latex]{ F }_{ Res }[/latex] =[latex]\sum { { F }_{ i }; } \quad { F }_{ Res }[/latex]=[latex]2({ F }_{ R }+{ F }_{ O }+{ F }_{ L }+{ F }_{ E })[/latex][latex]\quad \quad[/latex] [latex]{ F }_{ Res }[/latex]= [latex]270N[/latex]

[latex]{ M }_{ RO }[/latex]=[latex]\sum { { M }_{ Ox } } ;\quad [/latex] [latex]{ M }_{ RO }[/latex]=[latex]-2{ F }_{ R }a+2{ F }_{ E }c+2{ F }_{ L }b\quad \quad[/latex] [latex]{ M }_{ RO }[/latex]=[latex]-2.22N.m[/latex]

Question : A biomechanical model of the lumbar region of the human trun...

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