Design Principles

Basic Theory

Twisted string actuators (TSA) are often used to imitate a tendon-based driving system by converting the rotary motion of an electric motor into a linear tensile force. Due to its high reduction ratio, TSAs can be used with small and lightweight motors, useful in applications that limit size and weight. TSAs are commonly found in biomimetic robotic applications such as robotic hands and exoskeletons, acting as tendons that control the motions of limbs connected by a joint.

Twisted string actuators commonly consist of an electric motor, a string, a linear guide, and a load.

For the electric motor, we decided to use a NEMA 17 1.8 deg stepper motor. This is because a stepper motor can run on a pulsed current and with each pulse, it can turn fractions of a full rotation as opposed to a DC brushed motor that spins constantly for as long as the stator coils are energized. This main feature of a stepper motor allows for its shaft to rotates in steps, which can be very crucial for designs that required precise twisting.

The type of string being used plays a critical role in determining the strength and performance of the TSA. Due to the repeated twisting and untwisting of the string, the string endurance life often only lasts in the range of tens of thousands of cycles. Therefore, tougher materials like ultra-high molecular weight polyethylene or nylon fishing line are often used for bearing heavy loads and longer durability. However, for designs that do not endure a significant load, using standard crafting threads is satisfactory. Note that since crafting threads are typically double or triple in diameter of fishing lines, they required two to three times fewer steps/cycles from the motor to acquire significant contraction as compared to finishing lines.

A linear guide or a separator is necessary as it enables the string to contract by allowing one end to rotate while the other end to linearly translate with respect to each other. Further details of a separator are explained below.

Lastly, the load attached to the TSA must be able to translate linearly asin accordance with the contraction of the string. This typically appears in the form of a spring or a load on wheels that can move linearly. In biomimetic applications, this load can be a finger or a limb.

The force is produced by the shortening of the twisted bundle due to the twisting of one or more strings around itself/one another.

The separator/ linear guide allows for linear motion while prevents rotation past that point.

The linear motion of the actuator is produced by the shortening of the string as the motor twists the string into a bundle. The string in the TSA is attached to an electrical motor at one end and to a load on the other. Therefore, it needs to convert the rotary motion of an electric motor of one end into a linear tensile force in order to pull on the load at the other end. Since the entire string is subjected to the rotational motion of the motor, there needs to be a mechanism that can separate the string into a twisting zone and a linear zone. For this reason, a linear guide or separator is added that prevents the string from rotating beyond that point and allows the string to pass through to the other side where it moves only linearly.

Derivation

Governing Equations for Twisted String Actuators:

𝑟𝑣𝑎𝑟 is the radius of the twisted bundle is described by

𝑟𝑣𝑎𝑟 = 𝑟 ∙ √ (𝐿+∆𝑋)/ 𝐿 (1)

Where L is the length of the untwisted bundle, r is the radius of the untwisted bundle, and ∆𝑋 is the difference between the resting length of the twisted bundle and the current length.

∆𝑋 is described by

∆𝑋 = 𝐿 − √𝐿^2 + (𝜃^2 * 𝑟𝑣𝑎𝑟^2) (2)

Where θ is the number of turns of the bundle in radians.

F is the force generated by the bundle is described by

F = = 𝜏𝐿 /𝜃(𝑟𝑣𝑎𝑟 )^2 (3)

Where 𝜏 is the output torque of the motor.

The easiest approach is to define the required actuation length ∆𝑋 and use equation 1 and equation 2 to derive θ as

𝜃 = √ ((∆𝑋−𝐿)^2 − 𝐿^2 ) / 𝑟𝑣𝑎𝑟^2 (4)

Design Considerations

In designing your own TSA, there are a couple of alternatives to consider:

Twisting zone length: TSAs have a contraction ratio of 25% to 30% of the string untwisted length. Therefore, the amount of contraction is proportional to the length of the twisting zone (the distance between the motor and the linear guide). To increase the contraction, increase the twisting zone length.
String Materials: tougher materials like ultra-high molecular weight polyethylene or nylon fishing line offer longer durability and are useful for heavier loads. While materials like common strings and crafting threads typically have a much bigger diameter, allowing them to contract to the same length with two to three times fewer steps/cycles as compared to fishing lines.
Type of motor: A stepper motor offers a more precise twisting of the string and an easier method for keeping track of twisting cycles. A DC motor provides less precise twisting but is more accessible and is easier to control and operate. It is still a very adequate alternative for designs that simply need the contraction force of the TSA and not specific contraction lengths.

Separator styles: The separator plate is a flat plate with holes that allows the string to pass through while preventing any rotational movements beyond that point. The separator pin operates under the same principle. However, the string in the plate design is kept in place by the holes on the plate while the pin design mays allow the string to slip off. A 3D printed plate made of ABS plastic is cheap, easily manufactured, and possesses a low coefficient of friction with other plastics. It can also be made out of other materials, so long that the design is the same. If one does not have access to a 3D printer, the pin method is a possible alternative.

References

Mahmoud Tavakoli, Rafael Batista, Pedro Neto, "A compact two-phase twisted string actuation system: Modeling and validation, Mechanism and Machine Theory", Volume 101, 2016, Pages 23-35
May, Chris & Schmitz, Kai & Becker, Martin & Nienhaus, Matthias. "Investigation of Twisted String Actuation with a Programmable Mechanical Load Test Stand". 1-6. 2013
Bradley Scott Roan, "The effects of end termination on the endurance life of twisted string actuators." Department of Mechanical Engineering California State University, Sacramento, 2016
Rafael José Correia Batista, "A Compact Twisted String Actuation System for Robotic Applications," Department of Mechanical Engineering, Institute of Systems and Robotic of the University of Coimbra, 2014
J. Zhang et al., "Robotic Artificial Muscles: Current Progress and Future Perspectives," in IEEE Transactions on Robotics, vol. 35, no. 3, pp. 761-781, June 2019
Popov, D. & Gaponov, Igor & Ryu, Jee-Hwan. (2013). "A preliminary study on a twisted strings-based elbow exoskeleton," 2013 World Haptics Conference, WHC 2013. 479-484. 10.1109/WHC.2013.6548455.

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