section_path: Compound machines
section_name: Compound machines
paragraph_text: Compound machines
  
  A compound machine is a 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 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 gears (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
  
  M A compound = F out N F in1 {\displaystyle \mathrm {MA} _{\text{compound}}={F_{{\text{out}}N} \over F_{\text{in1}}}}
  
  Because the output force of each machine is the input of the next, F out1 = F in2, F out2 = F in3, … F out K = F in K + 1 {\displaystyle F_{\text{out1}}=F_{\text{in2}},\;F_{\text{out2}}=F_{\text{in3}},\,\ldots \;F_{{\text{out}}K}=F_{{\text{in}}K+1}}, this mechanical advantage is also given by
  
  M A compound = F out1 F in1 F out2 F in2 F out3 F in3 … F out N F in N {\displaystyle \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}}\,}
  
  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
  
  M A compound = M A 1 M A 2 … M A N {\displaystyle \mathrm {MA} _{\text{compound}}=\mathrm {MA} _{1}\mathrm {MA} _{2}\ldots \mathrm {MA} _{N}}
  
  Similarly, the efficiency of a compound machine is also the product of the efficiencies of the series of simple machines that form it
  
  η compound = η 1 η 2 … η N. {\displaystyle \eta _{\text{compound}}=\eta _{1}\eta _{2}\ldots \;\eta _{N}.}