For this weeks' Seek & Geek, I decided to analyse the "Lat Pulldown Machine" found in most gyms. It also happens to be one of my favorite pieces of gym equipment. Ironically, I had never noticed the number of pulleys on the machine. I found the arrangement of the pulleys to be interesting and wanted to delve deeper into the role of each pulley.

 

The Lat Pulldown machine is used to develop one's latissimus dorsi or "lat" muscle. It does this by requiring the user to pull a weight down from above his/her head, towards their chest. The weight being pulled can be adjusted appropriately. The weight creates tension along the cable which keeps the handle overhead. When a downward pulling force, greater than the tension is applied by the user, the weight move up while the handle moves down. Ideally, the lat muscles do all the work in lifting the weight up. However a lot of other muscles such as the back and shoulder muscles contribute to the effort.

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The cable system consists of eight pulleys and a cable whose one end is attached to the weight carriage and the other to the handle. The tension along the cable is constant at each point. 

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My first question were why so many pulleys and why not pass the cable over only pulleys 1 and 8? Or over 1, under 7 and over pulley 8?

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The only reason I could think of, was to preload the system. If the cable simply went over Pulleys 1 & 8, the cable would sag significantly when the user was not pulling down. This could cause the cable to slide out of the pulley and create an unpleasant experience for the user. Adequate preload ensures that the handle will always return to the same initial position. Overall, the preload would restrict the motion of the cable to a fixed plane.

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How do the extra pulleys prelaod the system?

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Pulleys 3-7 are idler pulleys. They keep the cable in tension through a holding torque that depends on the wrap angle of the cable around the pulley. Larger the wrap angle, larger the holding force. This relationship is described by the Capstan equation. Thus the extra pulleys preload the system by increasing the overall wrap angle of the cable.