Cable Mechanism Maths: Designing Against the Capstan Equation

Cable Mechanism Maths: Designing Against the Capstan Equation

I fell in love with cable driven mechanisms a few years ago and put together some of my first mechanical tentacles to celebrate. But only after playing with them did I start to understand the principles that made them work. Today I want to share one of the most important equations to keep in mind when designing any device that involves cables, the capstan equation. Let some caffeine kick in and stick with me over the next few minutes to get a sense of how it works, how it affects the overall friction in your system, and how you can put it to work for you in special cases.


A Quick Refresher: Push-Pull Cable Driven Mechanisms


But first: just what exactly are cable driven mechanisms? It turns out that this term refers to a huge class of mechanisms, so we’ll limit our scope just to push-pull cable actuation systems.


These are devices where cables are used as actuators. By sending these cables through a flexible conduit, they serve a similar function to the tendons in our body that actuate our fingers. When designing these, we generally assume that the cables are both flexible and do not stretch when put in tension.


Since these cables are flexible, they can only exhibit a pull force, not a push, so cables often come in pairs to actuate along both directions. Here, they’ll be opening and closing the jaws of the Chomper.


Here, the joystick controls the yellow jaw of our Chomper by means of two cables, either of which can be put in tension. One of the key ..