# How does this multiple-curve-beam flexural pivot work?

I found this in Handbook of Compliant Mechanisms (2013), page 162, or at the start of "Chapter 11, Elements of Mechanisms," subsection 11.1.2 Revolute

I don't understand how it's supposed to go from 1 to 2 when b rotates around c.

This element is a rotational flexural pivot constructed by three curved beams to achieve a large range of motion. Theoretically, this element will rotate without axial-drift motion, because of the symmetric arrangement about the axis.

(1) Rigid body a is fixed. Rigid body b rotates about c-axis.
(2) Deformed configuration
(3) Photo of the device.

It's unclear which part of the beam is attached to what. I can understand how one curved beam could switch its curvature (in general, like they do in bi-stable latches), but I don't see how they could both at the end of of the rotation end up curved in a way that's opposite to how they started.

How could c2/c3 go from the configuration in 1 to the configuration in 2 ?

Or could they be two different iterations of the same idea ? I can see how (1) or (2) would resist rotation of c around b, and snap it back to its original position. The text claims (2) is the deformed configuration though. I can also see how (1) with just c1, c3, c5 would deform to (1) with c0, c2, c4 if (b) was turning anti clockwise.

Also, what would be an ideal material to print this kind of compliant mechanism ?

• You might get a good answer for how it works at engineering.stackexchange.com - if you do, let us know, and we can probably recommend materials.
– Davo
Jul 31, 2020 at 17:10
• Im reading th ebook right now and it seems to be a bit diffuse on many of the examples. But i would posit that its a typo it should read derived not deformed. I will ct one as soon as our waterjet is again taking reservations. Aug 1, 2020 at 15:32
• The picture looks as if there is a printed back surface to which the central part is attached. If this is not a photo illusion, it would prevent the central part from flexing properly. There is a limit to the amount of torque this can transmit, but within the elastic limits of the material it looks like a good design for a shaft coupler. May print it of nylon or TPU. I think the two pictures are functional similar, but 2 is not the result of twisting B in 1.
– cmm
Aug 5, 2020 at 16:31

The picture looks as if there is a printed back surface to which the central part is attached. This can not be the case, since otherwise the curved members would not be able to flex. Everything inside the outer ring must be detached from the back shell.

Like all couplers, especially flexible couplers, there is a limit to the amount of torque the coupler can transmit. Within the elastic limits of the material this looks like a good design, and a good match for 3D printing. The forces are along the layers, not across the layers.

This looks like a good design for a rotary coupler. I'm resisting calling it a "shaft" coupler since neither side is equipped with any connection to a shaft. One could modify the design to have a larger central hub with a shaft hole (and set screw(s)). As it is, there is an implied method to hold the outer ring, and a fairly explicit three-pin adapter to drop into the open slots in the arms which connect to the center.

I would use ABS rather than PLA, although it depends on the stiffness you require and ability to sustein abuse. PLA is stiller than ABS, while ABS, within the elastic limits, is more compliant. I am not confident that either of these plastics would stand up to thousands of millions of flexures.

I would prefer to print this of TPU or Nylon. Both of these are tougher than ABS and PLA. They withstand greater flex with fewer problems with micro cracks and degradation. I have printed another shaft coupler of TPU, and it was both compliant and still.

It isn't possible to really nail down a material without knowing the application.

As to your question about one example being a transform of the other, I don't thing they are. The A and B drawings are similar in function, but are not stressed and unstressed versions of the same part. Either will work as a coupler.

• Thanks. I contacted one of the coauthor of the book (Larry Howell) and he was kind enough to send to the original paper from which the chapter in the book was derived. Those drawings are not from the original paper (and the description indeed doesn't make sense), and the paper shows that this device requires a torque that is linear to the angle of rotation of the inner part around the outer in the possible range of motion of the mechanism; also the deflection (rotation) is greater than other designs, and other designs also have their torque increase sub linearly... Simulated in ANSYS.. Sep 14, 2020 at 20:17

I would try and print it in PLA because it is quite flexible. ABS is harder in my experience and breaks more easily. If you are able to print PET, you should also try that for the same reasons. There might also be better materials I've never heard of, also please leave a comment if I'm wrong with anything.

• PLA breaks brittle, ABS breaks after deformation. Aug 2, 2020 at 15:33