Editing Simple machine (section)

==Compound machines==
A ''compound machine'' is a [[machine (mechanical)|machine]] formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example, a [[Vise|bench vise]] consists of a lever (the vise's handle) in series with a screw, and a simple [[gear train]] consists of a number of [[gear]]s ([[Wheel and axle|wheels and axles]]) connected in series.

The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine, that is

<math display="block">\mathrm{MA}_\text{compound}   =  {F_{\text{out}N} \over F_\text{in1}}</math>

Because the output force of each machine is the input of the next, <math>F_\text{out1} = F_\text{in2}, \; F_\text{out2} = F_\text{in3},\, \ldots \; F_{\text{out}K} = F_{\text{in}K+1}</math>, this mechanical advantage is also given by

<math display="block">\mathrm{MA}_\text{compound}  =  {F_\text{out1} \over F_\text{in1}} {F_\text{out2} \over F_\text{in2}} {F_\text{out3} \over F_\text{in3}}\ldots  {F_{\text{out}N} \over F_{\text{in}N}}  \,</math>

Thus, the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of the series of simple machines that form it

<math display="block">\mathrm{MA}_\text{compound} = \mathrm{MA}_1 \mathrm{MA}_2 \ldots  \mathrm{MA}_N</math>

Similarly, the efficiency of a compound machine is also the product of the efficiencies of the series of simple machines that form it

<math display="block">\eta_\text{compound} = \eta_1  \eta_2 \ldots \; \eta_N.</math>