Precise Motion With Compliant Mechanisms

To obtain a precise motion we usually go for high precision hardware; proper bearing, tight tolerances and machined components. For small movements however, we can take advantage of the elastic properties of the material itself, and carefully design a compliant mechanism!

Compliant mechanisms allow you to make a working component from a single block of material; this greatly reduces the number of parts (down to one!) and provides great accuracy (since now there is no need for loose coupling between holes and pins).

In this instructable we’ll review the basics of compliant mechanisms design and apply them to a linear guide. But if you just need the compliant linear guide above, I’ve made this online tool (SOL75) which already knows all the calculations that needs to be done, so you can just tell the software what you need ;)

3D printer, nuts and screws

Looking at the compliant hinge above, you might worry that it would just snap. This is a bit counter-intuitive, but actually the thinner the element, the lower the stress! The hinge has to be thin in order not to snap!

To make sense of this, consider the following: the hinge needs to bend up to a predetermined angle. The thicker the element, the more force it will take to bend it up to that angle. The force required to bend it is directly related to the stress in the material, so the higher the force, the higher the stress!

If the element is thin, we can bend it easily, and the stress in the material will be small. For the mathematically inclined, here is an approximation which can help to size the hinge correctly:

S = (3*E)/(4*l) * t*tan(theta)

Where S is the maximum stress in the hinge, E is the young modulus of the material, l is the length of the hinge and t its thickness. Theta is the rotation angle at which the hinge must bend without failure. As you can see, the larger t, the larger the stress. Once you have an estimate of the peak stress, you can choose a suitable combination of l, t, theta that doesn’t exceed the maximum stress for your material.

Now that you (hopefully) trust that the hinge will not fail, we’ll use it in a more useful project, a mechanical accuracy amplifier. By pushing on the input lever, you can control the position of the output in a very accurate manner.

Let’s break it down into its main components; you might see them in other compliant mechanisms!

The output shuttle is held in place by 4 long elements. This configuration makes it very easy for the shuttle to move laterally, but it prevents rotations and vertical translations. For small movements, this behaves as a linear guide.

The push rod connects the input lever to the output shuttle. When either moves, the rod will translate and rotate a bit. The longer the rod, the smaller the rotation, so by carefully sizing the rod we can neglect the rotation altogether.

The input motion is de-amplified by a lever; as we move the end of the lever, the rod is pushed laterally by a fraction of the input motion. This allows us to increase the precision of our movements!

Another great benefit of compliant mechanisms is that they require no assembly. In this case, we can have the 3D printer do all the work, just print it and you are done!

NB: Drawback
All this being said, there is one big disadvantage which we should keep in mind. To get wider motions, you will need longer elements and this often leads to rather large components when compared with traditional assemblies.

If you want to make your own, but don’t want to do the stress analysis, that’s ok. You can either try your luck and guess the length, thickness and maximum angle of your hinges, or use SOL75, which was built exactly to spare me (and you) from tedious computations!