Open AccessArticle

A Lightweight, Simple-Structure, Low-Cost and Compliant Twisted String Actuator Featuring Continuously Variable Transmission

Chanchan Xu

^1,2

Tong Liu

^1,2

Shuai Dong

Yucheng Wang

¹ and

Xiaojie Wang

^1,*

Institute of Intelligent Machines, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China

Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China

Author to whom correspondence should be addressed.

Actuators 2024, 13(12), 477; https://doi.org/10.3390/act13120477

Submission received: 29 September 2024 / Revised: 7 November 2024 / Accepted: 22 November 2024 / Published: 25 November 2024

(This article belongs to the Special Issue Actuator Technologies and Control: Materials, Devices and Applications)

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Graphical abstract
"> Figure 1
The TSA with a CVT mechanism. (a) The state without load. (b) The state with a small load. (c) The state with a large load. "> Figure 2
The proposed TSA with CVT, pre-twisted half a turn, for initial state without load (a) and with load (b). (c) The state with load after the motor makes a certain number of turns <math display="inline"><semantics> <mi>θ</mi> </semantics></math>. (d) Force analysis for CVT1. "> Figure 3
Theoretical TR of the proposed TSA with CVT varied with the number of turns of the motor and load <math display="inline"><semantics> <msub> <mi>F</mi> <mi>z</mi> </msub> </semantics></math>. "> Figure 4
The test platform for the properties of TSA with CVT. "> Figure 5
The performance test results of the proposed TSA with CVT. (a) The experimental and theoretical load contractions for the proposed TSA with CVT varied with the number of turns of the motor, maintaining a constant output speed of 12.5 rpm/min while carrying workloads of 0.1 kg, 0.5 kg, and 1.5 kg, respectively. (b) The experimental and theoretical average contraction speed of the load and average TR varied with the load, maintaining a constant motor output speed of 12.5 rpm/min. "> Figure 6
Snapshot of TSA with CVT carrying workloads of 0.1 kg, 0.5 kg, and 1.5 kg. (a) In the initial state and pre-twisted half a turn with the load. (b) After being twisted 7.5 turns from the initial state. "> Figure 7
The design principle of the proposed anthropomorphic robot finger with the proposed TSA with CVT. (a) The initial state for pre-twisted half a turn without load. (b) The state after grasping the object. "> Figure 8
Experimental setup to evaluate the proposed anthropomorphic robot hand. "> Figure 9
The results of the adaptability assessment of the proposed anthropomorphic robot hand. (a) illustrates the number of turns of the motor, the distance between the ends of the CVT and the string connection, the fingertip force provided by the spring, and the flexion angle of rotation of link 2 of the finger around joint 2 over time with a constant motor output speed of 60 rpm/min, respectively. (b) displays the motion states of the proposed anthropomorphic robot hand at time intervals of 0 s, 3.8 s, and 8.6 s. ">

Versions Notes

Abstract

Twisted string actuators, which are an emerging artificial muscle, efficiently convert rotary motor motion into linear load movement, with advantages like high transmission ratio, compliance, simple structure, and long-distance power transmission. However, the limited range of transmission ratio adjustment remains a challenge. Thus, this paper introduces a novel twisted string actuator design that automatically and continuously adjusts its transmission ratio in response to external loads. Utilizing lightweight hyperelastic slender rods, the twisted string actuator with continuously variable transmission achieves a simple, compact, and cost-effective design. By manipulating the distance between two twisted strings through rod deformation, the transmission ratio continuously adapts to varying load conditions. Mathematical models of the twisted string actuator with continuously variable transmission are derived and experimentally validated, demonstrating a 2.1-fold transmission ratio variation from 0.1 kg to 1.5 kg loads. Application in an anthropomorphic robot finger showcases a 6.2-fold transmission ratio change between unloaded and loaded states. Our twisted string actuator with continuously variable transmission offers unparalleled advantages in weight, cost, simplicity, compliance, and continuous transmission ratio adjustability, making it highly suitable for robotic systems.

Keywords:

twisted string actuator; continuously variable transmission; anthropomorphic robot finger

Graphical Abstract

1. Introduction

In robotic systems, the need for versatility means that robots often operate under varying conditions. For instance, when lifting heavy objects, a robot requires greater torque output, while for rapid movement, a higher speed output is necessary. A standalone motor excels at high efficiency under high speeds with low-torque conditions, but its performance deteriorates when high torque is required at low speeds. To enhance the motor’s load capacity while maintaining efficiency under high-torque conditions, it is common to pair the motor with a gearbox. However, this configuration often results in a significant reduction in speed under low-torque conditions. To simultaneously meet the demands for high speed and high torque, it is often necessary to use a motor with excessive power, which can lead to power redundancy and increased energy consumption. The development of continuously variable transmission (CVT) mechanisms is essential in enabling robotic systems to achieve both high-speed motion and substantial load capacity, thereby enhancing actuator efficiency [1]. Various CVT devices have been devised, encompassing wheel-type CVT, belt CVT, chain CVT, toroidal CVT, and spherical CVT, among others [2,3,4,5]. Each variant offers distinct approaches to achieving continuous variation in transmission ratio (TR), each with its own set of advantages and constraints.

Twisted string actuators (TSAs) represent a noteworthy soft actuator type, comprising one or more strings, an electric motor, and a load. They adeptly convert rotational motion from the motor into linear motion by winding the string(s). Owing to their straightforward design, high TR, substantial output force, and compliance, TSAs have found applications in a myriad of fields, including robotic hands, rehabilitation robots, and soft robots [6,7]. TSA effectively combines the functionalities of a motor and a gearbox, allowing it to operate efficiently under low speed with high-torque conditions; however, it operates within a relatively narrow efficient range. Thus, optimizing TSA performance necessitates integration with a CVT mechanism to tailor its TR in accordance with operational loads, typically achieved through modifications in string radius, string distance, or input torque.

Shin et al. [8] pioneered a passive dual-mode transmission mechanism rooted in TSA principles. In force mode, strings intertwine, while in speed mode, they rapidly coil around a thick shaft, effectively augmenting the string’s radius. Despite offering a wide transmission ratio range, mode switching is beset by uncertainty owing to time-varying friction, leading to significant energy loss. To mitigate this challenge, the team proposed an active dual-mode variable transmission (VT) by incorporating a secondary motor [9]. However, this solution comes at the expense of compliance and introduces complexity. Furthermore, the dual-mode VT merely offers discrete TR levels, lacking continuous adjustment. Lu et al. [10] realized continuous automatic TR adjustment predicated on external load variations by compressing springs to varying extents, thereby inducing the string to wind around a shaft of variable radius. Nevertheless, their mechanism, characterized by a complex architecture and friction-induced energy losses, presents notable drawbacks. Additionally, Park’s team [11] devised an elastomeric CVT-based TSA for automatic TR adjustment based on load size. Unlike Lu et al., they achieved continuous TR adjustment by modulating the input torque of the string according to the external load, accomplished by compressing the elastomer linked to the string’s end. Nonetheless, the torque transmission pathway, from the motor through spur gears to a rigid lateral disc, reliant on friction between the disc and elastomer, harbors the risk of energy dissipation, silicon abrasion, and slippage. Consequently, its viability for large robot devices is compromised by the inherent friction limitations of the elastomer. Similarly, Shin et al. [12] engineered a CVT-based TSA by manipulating the input torque of the string in response to the external load. While their CVT delivers a twofold increase in TR compared to Park’s team’s, its highly intricate and bulky nature renders it unsuitable for lightweight robots.

In the pursuit of a lightweight and simplistic TSA with a CVT system, Ryu’s team [13] introduced a passive TSA with CVT that adjusts TR by varying the distance between two strings using springs, contingent on external load fluctuations. Despite its relatively lightweight and straightforward design, the spring-based CVT still suffers from enlarged dimensions, rendering it less conducive for small robots. Moreover, to achieve continuous active TR adjustment, the team devised an active-type TSA with CVT employing planetary gears [14]. However, the incorporation of planetary gears and a secondary motor amplifies system weight, size, and cost, at the expense of compliance. Notwithstanding the plethora of TSA-based VTs developed, there persists a demand for a VT that is exceedingly lightweight, mechanically simple, compact, cost-effective, intrinsically compliant, continuous, and suitable for both small- and large-scale robotic applications.

To address this imperative, we present a novel TSA with CVT capable of continuously adjusting TR by modifying the distance between two twisted strings in response to external load variations. Our CVT comprises solely a pair of extremely lightweight hyperelastic slender rods, measuring a mere 1 mm × 1 mm × 32 mm, weighing 0.22 g, and costing only USD 0.041. Its TR undergoes a 2.1-fold variation as the load transitions from 0.1 kg to 1.5 kg. Comparative analysis against existing TSA-based VTs in Table 1 underscores our proposed TSA with CVT as the option that is lightest, simplest in structure, and most cost-effective. Furthermore, it boasts compliance and continuity, rendering it suitable for a plethora of robotic tasks across various scales. The proposed novel TSA with CVT system design significantly enhances the operational capabilities and broadens the potential applications of TSAs in diverse robotic contexts.

The subsequent sections are structured as follows: Section 2 elucidates the proposed design concept and operational mechanism of the TSA with CVT. Section 3 gives a theoretical analysis of the TSA with the CVT system. In Section 4, we delineate an experimental setup aimed at validating the efficacy of the proposed mechanism and the established theoretical model. Finally, in Section 5, we demonstrate the application of the proposed TSA with CVT to an anthropomorphic robot finger.

2. Concept of the Proposed TSA with CVT

Actuators employed in robotic systems are expected to exhibit a smaller TR for swift motion when operating without a load and a larger TR for delivering substantial supporting force at lower speeds when subjected to a load. To achieve this objective, we propose a TSA with CVT that automatically adjusts its TR according to the load weight. The structure and mechanism of the proposed TSA with CVT are illustrated in Figure 1. The proposed TSA with CVT consists of a pair of CVTs (CVT1 and CVT2) integrated within the TSA framework. CVT1 is linked to the motor’s output shaft, while CVT2 is connected to the load. Both CVT1 and CVT2 comprise hyperelastic rods, interconnected by two strings. When CVT2 bears a lighter load, it undergoes minimal deformation. The distance between the strings is large, allowing rapid contraction, resulting in a small TR. Conversely, under heavier loads, CVT2 undergoes bending deformation, reducing the distance between the strings and slowing down the contraction speed, thereby increasing the TR and enhancing load capacity. As the load magnitude increases, the bending deformation of CVT2 intensifies, resulting in a smaller string distance, further increasing the TR and enhancing the load capacity.

3. Theoretical Analysis for the Proposed TSA with CVT

In this section, we develop a mathematical model for the proposed TSA with CVT that describes the relationship between input and output displacements, thereby characterizing the TR of the entire system. Additionally, we verify the effectiveness of the proposed TSA with CVT through theoretical computational results.

3.1. Mathematical Model

The proposed TSA with CVT is a combination of TSA and CVT. Notably, the conventional mathematical model for TSA initially assumes the strings to be rigid, overlooking the fact that the strings possess stretchable properties. While the conventional model simplifies the modeling process, it compromises the model’s precision. Consequently, in our modeling approach, we consider the strings to be stretchable, with an associated stiffness coefficient denoted as K. Furthermore, we consider the CVT as a hyperelastic material, assuming its deformation to be within its elastic range and characterized by a constant elastic modulus E. To avoid an abrupt contraction of strings leading to an uncomfortable linear motion of load, the string is pre-twisted half a turn, as illustrated in Figure 2a. Once this pre-twisting is applied, we can calculate the initial distance, denoted as

X_{0}

, which represents the vertical distance between the connection points of the two CVTs and the strings on the same side, using the following formula:

X_{0} = \sqrt{L_{0}^{2} - D_{0}^{2}}

(1)

where

L_{0}

represents the initial length of the string without load force and

D_{0}

is the initial distance between the ends of the CVT and the string connection without load force. When a workload is attached to CVT2, as depicted in Figure 2b, the strings experience tension, causing them to stretch from

L_{0}

L_{1}

. This simultaneously induces bending deformations in CVT1 and CVT2, leading to a reduction in the distance between the ends of the CVT and the string connection from

D_{0}

D_{1}

and an increase in the vertical distance between the connection points of the two CVTs and the string on the same side from

X_{0}

X_{1}

As the motor rotates by an angle of

θ

, the strings undergo a corresponding twisting motion, forming a cylindrical shape with a radius of

r_{θ}

in their midsection, as depicted in Figure 2c. This results in an increase in the tension experienced by the strings, causing their axial length to transition from

L_{1}

L_{θ}

. Concurrently, CVT1 and CVT2 undergo further bending, resulting in a transition of the distance between the ends of the CVT and the string connection from

D_{1}

D_{θ}

. Ultimately, this leads to a decrease in the vertical distance between the connection points of the two CVTs and the strings on the same side to

X_{θ}

, thereby inducing a linear motion of the load denoted by

Δ X_{θ}

L_{θ}

can be calculated by

L_{θ} = L_{0} + \frac{F_{θ}}{K}

(2)

F_{θ} = \frac{F_{z}}{2 cos α_{θ}}

(3)

where

F_{θ}

represents the axial tension of the string when it is twisted by an angle of

θ

, and

F_{z}

represents the load force. Additionally,

α_{θ}

is the angle between the string and the motor axis direction when it is twisted by an angle of

θ

. We assume that the helix angle of the formed cylinder is evenly distributed across the twists of the strings; thus, the helix angle equals the angle between the string and the motor axis direction,

α_{θ}

. Now suppose one of the strings is the unwound geometry of a cylinder, as shown in Figure 2c;

cos α_{θ} = \frac{X_{θ}}{\sqrt{X_{θ}^{2} + {(D_{θ} + r_{θ} + θ r_{θ})}^{2}}}

(4)

X_{θ} = L_{θ} cos α_{θ} = L_{0} cos α_{θ} + \frac{F_{z}}{2 K}

(5)

The assumption of variable string radius was proved in [15]. However, given the elasticity of the strings, which experience deformation under tension, we have taken into account the impact of the applied load force on the radius. As a result, we approximate the radius

r_{θ}

of the cylindrical shape formed by the middle section of the strings using the following relationship:

r_{θ} = (\frac{1}{k_{1} F_{z}} + k_{2} + k_{3} \sqrt{X_{0} / X_{θ}}) r_{0}

(6)

where

k_{1}

k_{2}

, and

k_{3}

represent approximation coefficients that depend on the structure and mechanical properties of the strings, and

r_{0}

stands for the diameter of the string when they are in an unloaded state.

To determine

D_{θ}

, we conduct a force analysis on CVT1, as depicted in Figure 2d. CVT1 is fixed to the motor’s output shaft via a fixture of width c. The two ends of CVT1 experience bending deformation due to the tension in the two strings. Here, CVT is considered as a slender rod with a diameter d, which allows for the force and deformation characteristics of CVT1 to be likened to those of two symmetric cantilever beams, each subjected to concentrated loads at their endpoints. Therefore, we opt to analyze the force and deformation on the right half of CVT1. Select the center point of the right end face of the fixture as the coordinate origin O and assume that the entire assembly reaches equilibrium after the strings have twisted through an angle

θ

. We define the horizontal distance from any point C on the right half of CVT1 to O as x and the vertical distance to O as y. The resulting deformation of the bending curve satisfies the following flexural curve differential equation:

\frac{d^{2} y / d^{2} x}{{(1 + {(d y / d x)}^{2})}^{3 / 2}} = \frac{M}{E I}

(7)

where M represents the moment experienced at point C and I is the moment of inertia of the cross-section, where

I = \frac{π d^{4}}{64}

Point

A_{θ}

is the connection point between CVT1’s right end and the string, bearing a concentrated load

F_{θ}

applied by the string. Let

x_{θ}

denote the horizontal distance from point

A_{θ}

to the origin O, and let

y_{θ}

represent the vertical distance from point

A_{θ}

to the origin O. Thus, the coordinates of point

A_{θ}

can be expressed as (

x_{θ}

y_{θ}

). By breaking down the tension

F_{θ}

at point

A_{θ}

into horizontal force

F_{x θ}

and vertical force

F_{x θ}

, we have

\{\begin{matrix} F_{y θ} = F_{z} / 2 \\ F_{x θ} = F_{z} tan α_{θ} / 2 \end{matrix}

(8)

Consequently, the moment M experienced at point C can be calculated as follows:

M = F_{y θ} (x_{θ} - x) + F_{x θ} (y_{θ} - y)

(9)

Assuming that the shape of the right half of CVT1 forms a quadratic curve after deformation, the relationship between y and x is as follows:

y = a x^{2}

(10)

where a is the coefficient of the quadratic curve. Substituting (8)–(10) into (7), we obtain

\frac{2 a E I}{{(1 + 4 a^{2} x^{2})}^{3 / 2}} = F_{y θ} (x_{θ} - x) + F_{x θ} (a x_{θ}^{2} - a x^{2})

(11)

Assuming that the length of the right half of CVT1 remains unchanged before and after deformation, we have

2 \int_{0}^{x_{θ}} \sqrt{1 + {(2 a x)}^{2}} d x + c = D_{0}

(12)

Finally, the load contraction of the proposed TSA with CVT, represented by

Δ X_{θ}

, can be expressed as

Δ X_{θ} = X_{1} - X_{θ} - 2 Δ y_{θ} = X_{1} - X_{θ} - 2 (y_{θ} - y_{1})

(13)

where

y_{1}

represents the vertical distance between point

A_{θ}

and point O when the strings with load are twisted by half a rotation, and

Δ y_{θ}

is the distance by which point

A_{θ}

moves downward when the strings with load twist from half a rotation to

θ

. By solving Equations (5), (11) and (12) together, we can determine the values of

X_{θ}

and

y_{θ}

. Setting

θ = π

in these equations allows us to solve for

X_{1}

and

y_{1}

. Further, we can resolve

Δ X_{θ}

. Thus, the TR of the proposed TSA with CVT is expressed as follows:

T R = \frac{1}{\partial (Δ X_{θ}) / \partial θ}

(14)

3.2. Theoretical Results

We validate the effectiveness of the proposed TSA with CVT through theoretical analysis. Theoretical computational results depicting how the TR varies with the number of motor turns under various loads

F_{z}

are presented in Figure 3. The parameters utilized in the theoretical model are outlined in Table 2. It is observed that as the number of motor turns increases, the TR gradually decreases, consistent with the findings of Ryu’s team [13]. Additionally, under the same number of motor turns, the TR increases with increasing workload, which is particularly noticeable with lower loads. Under the initial condition of half a turn pre-twist, the TR increases from 2.95 rad/mm to 4.83 rad/mm with the load ascending from 1 N to 15 N, marking a 1.6-fold increase. Moreover, with a pre-twist of 7.5 turns from the initial state, the TR surges from 0.59 rad/mm to 1.89 rad/mm, demonstrating a 3.2-fold rise under the corresponding load conditions. For lighter loads, the TSA with CVT demonstrates lower TR, resulting in faster contraction speed. Conversely, for heavier loads, the TSA with CVT shows higher TR, leading to slower contraction speed but enhanced load capacity. Thus, the effectiveness of the designed TSA with CVT is theoretically confirmed.

4. Performance Evaluation for the Proposed TSA with CVT

In this section, we develop an experimental setup to test the performance of the designed TSA with CVT and experimentally confirm the effectiveness of the proposed TSA with the CVT mechanism. Additionally, we validated the previously established theoretical model by comparing the experimental and theoretical values of TSA’s contraction.

4.1. Experimental Setup

Figure 4 showcases the experimental setup utilized to assess the TR change capability of the TSA with CVT under varying loads. The key components of the setup included a direct current (DC) motor (Maxon DCX16L) controlled by an RMDS-405 motor driver, a pair of CVTs (CVT1 and CVT2), two strings, a load, a linear guideway (Hiwin, MG), and a linear variable differential transformer (LVDT, W-DC) with a stroke of 20 cm. The DC motor was horizontally mounted on a frame and operated via the RMDS-405 motor driver. The load and LVDT were securely affixed to the linear guide. We conducted experiments using parameters consistent with those listed in Table 2. For the CVTs, two Ni-Ti memory alloy rods with a diameter of 1 mm, a length of 32 mm, and an elastic modulus of 37 Gpa, exhibiting superelastic characteristics, were utilized. CVT1 was connected to the output shaft of the motor using a 6 mm wide fixture, while CVT2, also with a 6 mm wide fixture, was positioned parallel to CVT1 on the linear guide. Two braided ultra-high-molecular-weight polyethylene (UHMWPE) fiber strings, each with a diameter of 1.5 mm, an initial length of 97 mm without external loads and a stiffness coefficient of 1370 N/m, were employed for the TSA. These strings were connected at either end of CVT1 and CVT2 in parallel to the motor’s axis. To prevent sudden load movement, the strings were pre-twisted half a turn. Subsequently, the motor drove CVT1 to continuously rotate with a constant speed of 12.5 rpm/min for 7.5 turns under different loads.

4.2. Results

The performance test results of the proposed TSA with CVT are illustrated in Figure 5. In Figure 5a, the experimental and theoretical load contractions for the proposed TSA with CVT are depicted, showcasing variations in the number of motor turns across different loads. The tension parameters used in our models were experimentally measured from the materials employed in the actuator, ensuring that they accurately reflect the material properties under operating conditions. For the deformation parameters in the theoretical modeling, we utilized a curve-fitting approach based on experimental data to derive these values. It is observed that as the number of motor turns increases, the load contraction gradually increases. Under the same number of motor turns, the load contraction decreases with an increasing workload, which is particularly evident with a higher number of turns. The TSA with CVT exhibits maximum contractions of 34.9 mm, 22.1 mm, and 16.64 mm when carrying workloads of 0.1 kg, 0.5 kg, and 1.5 kg, respectively. Comparing load contraction, there is a 36.7 % decrease from 0.1 kg to 0.5 kg a 24.7 % decrease from 0.5 kg to 1.5 kg, and a 52.3 % decrease from 0.1 kg to 1.5 kg. The TSA with CVT exhibits greater sensitivity to load variations between 0.1 kg and 0.5 kg compared to between 0.5 kg and 1.5 kg.

Additionally, Figure 5b illustrates experimental and theoretical data concerning the average contraction speed of the load and the average TR as they vary with the load. The average contraction speed of the load represents the TSA’s operational speed, and the operational speed of the TSA is inherently linked to the TR, which is the ratio of the motor speed to the load movement speed. When the motor operates at a constant speed, an increase in the TR results in a decrease in the TSA’s operational speed. Firstly, we can find that the theoretical average contraction speed of the load and the average TR closely align with experimental results. Moreover, there is a decreasing trend in the average contraction speed of the load with increasing workload, while the average TR of the TSA with CVT exhibits a corresponding increase with workload. Under loads of 0.1 kg, 0.5 kg, and 1.5 kg, the TSA with CVT demonstrates experimental average contraction speeds of 0.97 mm/s, 0.61 mm/s, and 0.46 mm/s, respectively. Correspondingly, the experimental average TR varies at 1.35 rad/mm, 2.13 rad/mm, and 2.83 rad/mm for these respective loads. Notably, under a 1.5 kg load, the experimental contraction speed diminishes to 47.4% of that observed under a 0.1 kg load, while the average TR increases to 2.1 times. When the load is lighter, the TSA with CVT demonstrates reduced TR, facilitating quicker contraction rates. Conversely, under heavier loads, the TSA with CVT displays elevated TR, resulting in slower contraction rates but increased load capacity.

This phenomenon is demonstrated in Figure 6, which presents snapshots of the TSA with CVT carrying loads of 1 kg, 0.5 kg, and 1.5 kg in the initial state with half a turn of pre-twist with the load (Figure 6a) and subsequent to being twisted 7.5 turns from the initial state (Figure 6b). In Figure 6a, it is observed that when the load is 0.1 kg, the CVT undergoes minimal deformation in the initial state, with the distance between the ends of the CVT and the string connection (D) being 32 mm. With increasing turns, D remains almost unchanged, indicating that the CVT effectively operates as if under a fixed offset of 32 mm, resulting in relatively faster contraction speeds. When the load is 0.5 kg, there is a slight change in the CVT from 32 mm to 31 mm in the initial state, indicating a smaller change compared to the 0.1 kg load. However, as the turns increase, the tension on the string gradually increases, causing the CVT to bend and D to decrease while increasing the downward displacement (

Δ y_{θ}

) of the ends of the CVT and the string connection. D decreases to 28.9 mm after 7.5 motor turns. The comprehensive effect of load contraction resulting from both the contraction of the string (

X_{1} - X_{θ}

) and the downward displacement of the CVT (

Δ y_{θ}

) due to bending, is described by Equation (13). A larger (

X_{1} - X_{θ}

) leads to faster load contraction, while a larger

Δ y_{θ}

results in slower load contraction. As D decreases with increasing turns, accompanied by an increase in

Δ y_{θ}

, there is a dual reduction in the load contraction speed, which becomes more pronounced with higher load. When the load increases to 1.5 kg, the CVT exhibits significant initial bending, reducing D to 29.2 mm, which further decreases to 25.9 mm after 7.5 motor turns, resulting in even slower load contraction. Therefore, the experiments demonstrate that the proposed TSA with CVT can automatically adjust TR according to external load variations to meet the system’s requirements.

Moreover, from Figure 6a, it is evident that our established theoretical model aligns well with experimental results. While the theoretical model almost coincides with experimental data for a 0.1 kg load, there are slight deviations for 0.5 kg and 1.5 kg loads during the initial twisting stage, likely due to gaps within the braided string and the nonlinearity of the elastic modulus of the superelastic materials used in the CVT under a higher load. Overall, our established model effectively predicts the load contraction of TSA with CVT. This model serves as a valuable theoretical tool for analyzing and optimizing the performance of TSA with CVT.

5. Application for an Anthropomorphic Robot Finger

In this section, we apply the proposed TSA with CVT to an anthropomorphic robot finger and test its adaptability to the external load, further validating the practicality of the proposed TSA with CVT.

5.1. Design and Working Mechanism

Figure 7 illustrates the design principle of the proposed anthropomorphic robot finger with the proposed TSA with CVT. The anthropomorphic robot finger comprises a 3D-printed finger including four links and three rotating joints, and the TSA with the CVT system. Link 0 is fixed, while links 1, 2, and 3 can rotate around joints 1, 2, and 3 respectively, with all three joints equipped with elastic rings to provide resilience. To prevent rotation at the output end of the CVT system, only a superelastic rod is employed near the motor end, while a fixed offset is utilized near the load end. The output end of the CVT system is connected to the fingertip via a tendon. The finger’s flexion is driven by the contraction force of the strings when the motor twists them, while the extension is achieved through the rebound force of the elastic rings at joints when the strings are untwisted.

The mechanism of the anthropomorphic robot hand with proposed TSA with CVT operates as follows: when the finger is not in contact with a load, the contraction force of the strings is minimal, and the CVT remains nearly unchanged. The distance between the strings is large, allowing rapid contraction, resulting in a small TR, thereby enabling the finger to quickly make contact with an object. Once the finger contacts an object, the contraction force of the strings increases, causing the CVT to bend and deform, reducing the distance between the strings and slowing down the speed of contraction. Consequently, the TR of the entire system increases, resulting in slower grasping speed but enhanced gripping capability. As the load increases, the degree of bending and deformation of the CVT becomes more pronounced, further reducing the distance between the strings and increasing the overall TR. Therefore, the anthropomorphic robot finger can adjust its TR according to the operational load conditions.

5.2. Performance Evaluation

To assess the TR change capability to a variable load of the proposed anthropomorphic robot finger, we designed an experimental setup as depicted in Figure 8. The motors (Maxon DCX16L) equipped with encoders (Maxon ENX16) were controlled using an RMDS-405 driver. The distance between the strings with a fixed offset is 30 mm. A superelastic Ni-Ti memory alloy rod with an initial length of 30 mm and a diameter of 1 mm was employed for CVT. The distance between the fixed offset and CVT is 86 mm. The string diameter is 1.5 mm. Given the varied motion trajectories inherent to underactuated robot fingers and the experimental objective of evaluating their capability to adapt to variable loads, joints 1 and 3 were immobilized, allowing only joint 2 to rotate freely. Consequently, an angle sensor (Inertial Measurement Units; IMUs) was affixed to link 3 to monitor the real-time flexion angle of link 2 around joint 2. A spring, connected at one end to the fingertip and at the other end to a tension sensor (SBT674 with a force of 50 N) secured on the frame, was utilized to provide the loading force. To prevent sudden finger movements, the string was pre-twisted half a turn. Subsequently, the motor drove the CVT to continuously rotate with a constant speed of 60 rpm/min for 8.5 turns. This caused link 2 to gradually rotate around joint 2 from a vertical position, gradually stretching the spring from its relaxed state. Both the IMU and tension sensor concurrently recorded data throughout the entire process.

The findings, presented in Figure 9, encompass various facets of the experiment. Figure 9a, from top to bottom, shows the number of motor turns, the distance between the ends of the CVT and the string connection, the fingertip force provided by the spring, and the flexion angle of rotation of link 2 of the finger around joint 2 over time, respectively. Figure 9b showcases the sequential motion states of the proposed anthropomorphic robot hand at time intervals of 0 s, 3.8 s, and 8.6 s (further details in https://1drv.ms/v/s!AgaftTaT7Nn_gQKCWWQmciREtH1j?e=Z5P5xD (accessed on 25 September 2024)).

It is evident that before t = 3.8 s, the spring is relaxed, providing zero force to the fingertip, and the distance between the ends of the CVT and the string connection remains almost constant. The average flexion speed of link 2 rotation around joint 2 is 10.36 degrees/s, except for the negligible motion because the initial twisting of the string does not significantly affect the movement of link 2. After t> 3.8 s, the spring gradually stretches, and the fingertip force increases from 0 N to 5 N. The distance between the ends of the CVT and the string connection is reduced to 12.4 mm, and the average flexion speed of the finger decreases to 1.67 degrees/s, indicating a notable 6.2-fold TR alteration between unloaded and loaded conditions. Additionally, from Figure 9b, it is apparent that before the stretching of the spring, the distance between the ends of the CVT and the string connection remains nearly constant. However, after the stretching of the spring, this distance noticeably decreases. The finger’s movement speed is significantly faster before the spring stretching compared to after. Therefore, the proposed anthropomorphic robot hand demonstrates the TR change capability to adapt to variable loads. It also exhibits a considerable adjustment range and can withstand at least 5 N of fingertip force. This underscores the practicality of the proposed TSA with the CVT concept.

6. Conclusions and Future Work

In conclusion, this paper has introduced a novel TSA with CVT, offering automatic adjustment of TR in response to varying external loads. Through the utilization of lightweight hyperelastic slender rods, we have achieved a remarkably simple, compact, and cost-effective design. Our experimental results have validated the efficacy of the proposed TSA with CVT, demonstrating a notable 2.1-fold TR variation across load conditions ranging from 0.1 kg to 1.5 kg. Notably, the hyperelastic rods utilized in our CVT are exceptionally lightweight and cost-efficient, with dimensions of just 1 mm × 1 mm × 32 mm, weighing 0.22 g, and costing only USD 0.041. An application in an anthropomorphic robot finger has further underscored the adaptability and practicality of our TSA with CVT, revealing a significant 6.2-fold TR change between unloaded and loaded states.

This research represents a significant advancement in the field of robotic transmission systems, offering unparalleled benefits in terms of weight, cost-effectiveness, simplicity, compliance, and continuous TR adjustability. The proposed TSA with CVT holds great promise for a wide range of robotic applications, from small-scale robots to complex anthropomorphic robotic hands. Future work will focus on refining theoretical models to account for nonlinear material characteristics and the over-twist phase that occurs beyond 7.5 turns. Additionally, we aim to expand the application of our TSA with CVT to a fully anthropomorphic robotic hand.

Author Contributions

Conceptualization, C.X. and S.D.; methodology, C.X.; software, T.L.; validation, C.X. and Y.W.; formal analysis, T.L.; investigation, C.X.; resources, X.W.; data curation, X.W.; writing—original draft preparation, C.X.; writing—review and editing, C.X. and X.W.; visualization, C.X.; supervision, C.X.; project administration, S.D.; funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript.

Funding

This work is partially supported by the Anhui Provincial Key Research and Development Program No. 2022f04020008 and National Natural Science Foundation of China No. 62301522.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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Figure 1. The TSA with a CVT mechanism. (a) The state without load. (b) The state with a small load. (c) The state with a large load.

Figure 2. The proposed TSA with CVT, pre-twisted half a turn, for initial state without load (a) and with load (b). (c) The state with load after the motor makes a certain number of turns

θ

. (d) Force analysis for CVT1.

Figure 2. The proposed TSA with CVT, pre-twisted half a turn, for initial state without load (a) and with load (b). (c) The state with load after the motor makes a certain number of turns

θ

. (d) Force analysis for CVT1.

Figure 3. Theoretical TR of the proposed TSA with CVT varied with the number of turns of the motor and load

F_{z}

Figure 3. Theoretical TR of the proposed TSA with CVT varied with the number of turns of the motor and load

F_{z}

Figure 4. The test platform for the properties of TSA with CVT.

Figure 5. The performance test results of the proposed TSA with CVT. (a) The experimental and theoretical load contractions for the proposed TSA with CVT varied with the number of turns of the motor, maintaining a constant output speed of 12.5 rpm/min while carrying workloads of 0.1 kg, 0.5 kg, and 1.5 kg, respectively. (b) The experimental and theoretical average contraction speed of the load and average TR varied with the load, maintaining a constant motor output speed of 12.5 rpm/min.

Figure 6. Snapshot of TSA with CVT carrying workloads of 0.1 kg, 0.5 kg, and 1.5 kg. (a) In the initial state and pre-twisted half a turn with the load. (b) After being twisted 7.5 turns from the initial state.

Figure 7. The design principle of the proposed anthropomorphic robot finger with the proposed TSA with CVT. (a) The initial state for pre-twisted half a turn without load. (b) The state after grasping the object.

Figure 8. Experimental setup to evaluate the proposed anthropomorphic robot hand.

Figure 9. The results of the adaptability assessment of the proposed anthropomorphic robot hand. (a) illustrates the number of turns of the motor, the distance between the ends of the CVT and the string connection, the fingertip force provided by the spring, and the flexion angle of rotation of link 2 of the finger around joint 2 over time with a constant motor output speed of 60 rpm/min, respectively. (b) displays the motion states of the proposed anthropomorphic robot hand at time intervals of 0 s, 3.8 s, and 8.6 s.

Table 1. The performance comparison with other existing TSA-based VTs.

TSA-Based VT Types	Weight of VT (g)	Size of VT (mmmmmm)	Complexity of VT’s Structure	Cost of VT ($)	Compliant?	Continuous?	Range of TR Adjustment
Our CVT	0.22	1130	Very simple	0.041	Yes	Yes	2.1 times
Dual-mode Passive [8]	>10	-	Moderate	>1	No	No	-
Dual-mode Active [9]	>29.6	69.219.515	Complex	>214	No	No	6.95 times
PVT [13]	80	>154080	Simple	>1	Yes	Yes	<2 times
ElaCVT [11]	12	242442	Complex	>10	Yes	Yes	2.31 times
Pat-CVT [12]	1400	85120.5115	Very complex	>10	Yes	Yes	4.6 times
Active CVT [14]	133.6	4545129	Complex	>232	No	yes	1.78 times
LAHM [10]	>10	141467	Complex	>1	Yes	Yes	2.1 times

Table 2. The parameters used in theoretical model.

$L_{0}$ (m)	$D_{0}$ (m)	c (m)	$r_{0}$ (m)	d (m)	K (N/m)	E (GPa)	$k_{1}$ (1/N)	$k_{2}$	$k_{3}$
0.097	0.032	0.006	0.0015	0.001	1370	37	7.1	0.22	0.224

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Xu, C.; Liu, T.; Dong, S.; Wang, Y.; Wang, X. A Lightweight, Simple-Structure, Low-Cost and Compliant Twisted String Actuator Featuring Continuously Variable Transmission. Actuators 2024, 13, 477. https://doi.org/10.3390/act13120477

AMA Style

Xu C, Liu T, Dong S, Wang Y, Wang X. A Lightweight, Simple-Structure, Low-Cost and Compliant Twisted String Actuator Featuring Continuously Variable Transmission. Actuators. 2024; 13(12):477. https://doi.org/10.3390/act13120477

Chicago/Turabian Style

Xu, Chanchan, Tong Liu, Shuai Dong, Yucheng Wang, and Xiaojie Wang. 2024. "A Lightweight, Simple-Structure, Low-Cost and Compliant Twisted String Actuator Featuring Continuously Variable Transmission" Actuators 13, no. 12: 477. https://doi.org/10.3390/act13120477

APA Style

Xu, C., Liu, T., Dong, S., Wang, Y., & Wang, X. (2024). A Lightweight, Simple-Structure, Low-Cost and Compliant Twisted String Actuator Featuring Continuously Variable Transmission. Actuators, 13(12), 477. https://doi.org/10.3390/act13120477

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A Lightweight, Simple-Structure, Low-Cost and Compliant Twisted String Actuator Featuring Continuously Variable Transmission

Abstract

1. Introduction

2. Concept of the Proposed TSA with CVT

3. Theoretical Analysis for the Proposed TSA with CVT

3.1. Mathematical Model

3.2. Theoretical Results

4. Performance Evaluation for the Proposed TSA with CVT

4.1. Experimental Setup

4.2. Results

5. Application for an Anthropomorphic Robot Finger

5.1. Design and Working Mechanism

5.2. Performance Evaluation

6. Conclusions and Future Work

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

References

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