Question

Explain why the forces in our joints are several times larger than the forces we exert on the outside world with our limbs. Can these forces be even greater than muscle forces (see previous Question)?

Short answer

Limbs in human bodies act as a third-class lever. The mechanical advantage is less than 1.

Step-by-step solution

Concept

Action of Human Hand

The human hand acts as a machine, i.e., a third-class lever.

The action of muscles when an object is placed on human hand palm is depicted as below:

Human hand as third-class lever

The arm is represented by EP, Elbow at E, palm at P. The load of weight L is at palm. The weight of the forearm is W.

The muscles exert a force\({F_M}\) upward, at a distance\({l_1}\) from E. The center of mass of the forearm and the load are at distances\({l_2}\) and\({l_3}\) from E.

Solving further

Calculation of force

Under the equilibrium of forces, we can write,

\({F_M} = {F_E} + W + L.......(1)\)

Under the equilibrium of the moments about the point E,

\(\begin{array}{c}{F_m}{l_1} = W{l_2} + L{l_3}\\{F_M} = W\left( {\frac{{{l_2}}}{{{l_1}}}} \right) + L\left( {\frac{{{l_3}}}{{{l_1}}}} \right)\;........(2)\end{array}\)

We can write from equation (1) that,

\(\begin{array}{l}{F_E} = {F_M} - (W + L)\\ = W\left( {\frac{{{l_2}}}{{{l_1}}}} \right) + L\left( {\frac{{{l_3}}}{{{l_1}}}} \right) - \left( {W + L} \right)\\ = W\left( {\frac{{{l_2}}}{{{l_1}}} - 1} \right) + L\left( {\frac{{{l_3}}}{{{l_1}}} - 1} \right)\end{array}\)

As the factors,\(\left( {\frac{{{l_2}}}{{{l_1}}} - 1} \right)\)and \(\left( {\frac{{{l_3}}}{{{l_1}}} - 1} \right)\)are greater than unity,

\({F_E} > W + L\)