The Challenge of Tuning Compliant Torsional Springs

by Arunachalam Thiraviam

Figure 1: Torsional spring

The green object in Figure 1 is a type of compliant torsional spring. Although it does not resemble a conventional helical spring used in many mechanical devices, it has a similar function: offering resistance to an external force.

In contrast to helical springs that resist compression or tension through their geometry, compliant torsional springs resist torsion. The amount of resistance is a function of the thickness of the spring arms.

Tuning the characteristics of this spring with conventional prototyping tools is a challenging and interesting problem.


Here is a short video of compliant iris actuation:

These springs belong to a group called compliant mechanisms, which offer mechanical resistance through their geometry and have a simple purpose: transfer a force or displacement from one link to the next through shape deformation. A compliant mechanism is best understood when compared and contrasted to its counterpart, a rigid mechanism. An example of a rigid mechanism is a gripper or a scissor lift.

A rigid mechanism relies on a set of parts connected by joints (hinges or pins) that enable relative motion between these links. A compliant mechanism relies on the flexibility of the design to execute these motions. The compliant gripper in Figure 3a relies on thin plastic hinges to perform the gripping action similar to its rigid counterpart shown in Figure 3b. The rigid surgical gripper requires two separate arms and a pin for the same action.


At even tiny sizes, compliant mechanisms can transfer forces. Since they have significantly fewer parts and movable joints, they have many uses as sensors and actuators in micro-electromechanical systems (MEMs).

The other advantages of compliant mechanisms are ease of manufacturing and maintenance. As many of these mechanisms have a few parts (some just have one, such as the spring), the manufacturing cost and time are lower in comparison to their rigid counterparts. Without moving parts, the need for lubrication and joint replacements is eliminated. This can significantly lower operational costs.


Figure 4 – (3D printing courtesy of Thom Hokama, RP Service Bureau, Operations Lead, Seattle, WA)

Additive manufacturing technology has enabled engineers to manufacture complex geometry with metals and plastics.

Printing the mechanism shown in Figure 4 was a far more viable alternative to injection molding owing to the narrow arms and the clearances between the moving parts.

This enables the user to scale the part based on its application without the need to redesign any tooling for its manufacture.

Access to 3D printing technology such as the FDM and PolyJet enables the use of a wide variety of real and digital plastic materials for printing. 3D printing software enables users to control layer density and the print path to optimize the weight and strength of the final print.

The model shown in Figure 4 was printed with an ASA material at a 0.005 in resolution on a STRATASYS Fortus 400 FDM printer with slightly modified layer properties to achieve maximum density on the slender iris arms.


Figure 5a

Finite Element Analysis (FEA) technology enables easy verification of the structural strength of the slender arms and the stiffness of the overall spring before manufacturing.

Figure 5a represents the stress distribution on the spring during actuation determined through FEA.

Figure 5b indicates the force required for the spring actuation. Using this data, the thickness of the spring arms was set to achieve a certain stiffness without compromising the spring’s structural strength.

Figure 5b

Figure 5a shows that the critical areas that govern strength are at the outer fibers of the arms and the connection between the arms and the outer ring. Notice also the characteristic of the force-displacement curve indicating the nonlinear stiffness of the spring.

FEA tools, such as SOLIDWORKS Simulation, provide valuable feedback. This enables engineers to confidently make changes to existing products or to design new ones.

Please let me know if you have questions or ideas in the comments section below.

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