Variable Stiffness Joint Research Articles

Reconfigurable origami with variable stiffness joints for adaptive robotic locomotion and grasping.

With its compactness and foldability, origami has recently been applied to robotic systems to enable versatile robots and mechanisms while maintaining a low weight and compact form. This work investigates how to generate different motions and shapes for origami by tuning its creases' stiffness on the fly. The stiffness tuning is realized by a composite material made by sandwiching a thermoplastic layer between two shape memory polymer layers. This enables the composite to act as a living hinge, whose stiffness can be actively controlled through Joule heating. To demonstrate our concept, we fabricate an origami module with four variable stiffness joints (VSJs), allowing it to have freely controlled crease stiffnesses across its surface. We characterize the origami module's versatile motion when heating different VSJs with different temperatures. We further use two origami modules to build a two-legged robot that can locomote on the ground with different locomotion gaits. The same robot is also used as an adaptive gripper for grasping tasks. Our work can potentially enable more versatile robotic systems made from origami as well as other mechanical systems with programmable properties (e.g. mechanical metamaterials).This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Design and control of variable stiffness joint based on magnetic flux adjustment mechanism

Design and control of variable stiffness joint based on magnetic flux adjustment mechanism

Mechanical Design of Variable Stiffness Joint Based on Planetary Gear Train and Modular Elastic Element

Methods:: By referring and combining existing mechanical design ideas of some series configuration VSJs with good stiffness adjustment mechanism schemes, a novel series configuration VSJ based on an equivalent lever mechanism and relying on adjusting the position of the lever pivot to change joint stiffness has been implemented through CAD drawing, 3D printing, and assembly. Results:: Due to the wide movable range of the lever pivot, the designed VSJ has a wide adjustable range of stiffness. Moreover, assembly design and modular design have been achieved in terms of elastic output and power transmission, for easy installation and maintenance. The movability and stiffness adjustability of the designed VSJ were preliminarily verified through manual adjustment. Conclusion:: The assembly model of the VSJ demonstrates the feasibility of structural design. The stiffness adjustment experiment showed the variable stiffness ability of the designed VSJ.

Design and Analysis of a Novel Variable Stiffness Joint Based on Leaf Springs

In response to challenges like the complexity and limited scalability of existing variable stiffness joints, a novel variable stiffness joint, based on leaf spring elements, is introduced in this paper. The joint stiffness can be adjusted in real time by changing the effective length of the leaf spring via the use of an Archimedean spiral groove. The stiffness adjustment range and load capacity of the joint can be defined by manually configuring the number of springs involved during offline joint operations. A stiffness model for the joint is established based on the cantilever beam theory of material mechanics. The coupled effects of the design parameters of the variable stiffness mechanism on joint stiffness, elastic torque, and stiffness adjustment resistance torque are analyzed. A dynamic model for the joint is developed, while a PID controller is designed for simulation purposes. The motion characteristics of the joint are analyzed, confirming that this approach has certain advantages in terms of stiffness adjustment speed and accuracy.

A novel stiffness-controllable joint using antagonistic actuation principles

The inherent safety of collaborative robots is essential for enhancing human–robot interaction. The primary challenge in creating soft components for these robots is achieving sufficient force and stiffness. This paper presents a joint design for collaborative robots that addresses this challenge by incorporating an antagonistic actuation principle, allowing for adjustable stiffness. The novelty of our variable-stiffness joint lies in achieving a wide range of stiffness variation at any bending angle through antagonistic actuation. This bio-inspired principle results from the activation of two opposing actuation chambers. Compared to existing joints, our proposed joint is compact and utilises a high percentage of soft materials, enabling safer human–robot interaction. The paper outlines the joint’s design and fabrication process, highlighting the feasibility of our innovative concept. Kinematic and stiffness models are introduced to analyse the bending and stiffness characteristics, which are further validated through experimental testing. The stiffness experiments demonstrate significant stiffness changes achievable through the antagonistic actuation principle. Additionally, force experiments reveal our joint can generate 20 N force at a 1.5×105 Pa pressure. A constant force output experiment confirms the joint’s advantages in providing consistent force compared to motors. Finally, a case study showcases how our proposed joint can be embedded in serial robots with variable stiffness capabilities under loading and safe human–robot interaction.

Kinetostatic Analysis of a Spatial Cable-Actuated Variable Stiffness Joint

Abstract The demand for robots capable of performing collaborative tasks requiring interactions with the environment is on the rise. Safe interactions with the environment require attributes such as high dexterity and compliance around obstacles, while still maintaining the requisite stiffness levels for payload manipulation. Such attributes are inherent to biological musculoskeletal systems. Motivated by this realization, this paper proposes a cable-actuated spatial joint with variable stiffness, inspired by the tensegrity principles found in biological musculoskeletal systems. The paper provides a detailed analysis of the joint’s mobility and mechanism kinematics. Based on the limits of the actuation forces, the paper also presents the wrench-feasible workspace of the joint. The paper also outlines the conditions that the cable actuation forces must satisfy to maintain the static equilibrium of the joint. The stiffness modeling presented in this work demonstrates the modulation of stiffness bounds as a function of cable actuation forces. Furthermore, the stiffness modulation as a function of the geometrical parameters is also presented.

Joint angle prediction for a cable-driven gripper with variable joint stiffness through numerical modeling and machine learning

Soft grippers in automation, particularly those with variable joint stiffness, offer promising possibilities for precise manipulation tasks. However, accurately predicting finger joint bending angles in this field poses significant challenges due to the soft and complex nature of the grippers, making modeling and angle prediction difficult. This paper presents the development of a predictive model for precisely controlling bending angles in multi-material printed soft grippers with variable stiffness, which are pivotal for delicate manipulation tasks in automation. In particular, we explore a cable-driven gripper design made of thermoplastic polyurethane and conductive polylactic acid materials, featuring integrated resistive joints for stiffness modulation through controlled Joule heating. A data-driven modeling approach, combining numerical modeling of the gripper and machine learning techniques, was employed for the development of the predictive model. We performed static structural simulations using ANSYS Workbench to measure bending angles under various conditions for developing datasets for model training. In this work, we evaluated several machine learning models such as linear regression, decision tree, and K-nearest neighbor regression models to predict the correlation between temperature, pull distance, and bending angle. The K-nearest neighbor regression model demonstrated the highest accuracy, with a mean absolute error of approximately 11%. These findings underline the importance of precise angle prediction models in enhancing the functionality and reliability of soft grippers, paving the way for their broader application in automation and robotics.

Design and analysis of a novel variable stiffness joints with robots

This paper presents the design of a symmetric variable stiffness joint that employs worm gear and sliding helical transmissions to adjust the effective length of the leaf springs. Firstly, the design concept and working principle of the variable stiffness joint are presented, along with two different assembly methods. Secondly, the stiffness equations and characteristics of the variable stiffness joint are then derived and analyzed. Next, the dynamics of the variable stiffness joint are modeled and simulated visually using Simulink. Finally, a prototype of the variable stiffness joint is constructed and its stiffness characteristics are experimentally verified. The experimental results demonstrate that both assembly methods are capable of adjusting the stiffness and position of the joint within a certain range. This study contributes to the understanding and development of symmetric variable stiffness joints by presenting a comprehensive design, analysis, simulation, and experimental evaluation. The proposed joint has potential applications in various fields that require adaptability, adjustability, and safety.

Coupled vibration analysis of bolted variable angle tow plates under combined nonlinear effects

To establish a dynamical modal of variable angle tow (VAT) plate accurately, the fiber path and fiber orientation of the VAT plate are described by high-order polynomials. Then, a simplified nonlinear joint model with interface dynamic partitioning is proposed to simulate the interface mechanical behavior of bolted joints. Based on these, a nonlinear semi-analytic dynamic model of the bolted VAT plate is built, which considers both material and joint nonlinearity and can accurately predict nonlinear vibration response. After verifying the proposed modeling method, a special bolted VAT plate is used as the analysis object for free vibration and forced vibration analysis. Firstly, the frequency veering behavior of the VAT plate caused by variations in boundary stiffness, connection stiffness, and fiber orientation is studied. Then, by analyzing the forced vibration response of the bolted VAT plate, it is found that under the combined effect of the modal interaction, material nonlinearity, and joint nonlinearity, the bolted VAT plate exhibited complex but rule-based nonlinear dynamic behavior. More importantly, the research work done in this paper has certain guiding significance for the optimization design of vibration resistance of a bolted VAT thin-walled structure with variable stiffness parameters and joint parameters as design variables.

Pose-dependent natural frequency prediction for milling robot—A variable joint stiffness model

Low prediction accuracy of natural frequencies of a milling robot is one major obstacle to the avoidance of chatter vibration in low-speed robotic milling. For enhanced accuracy in predicting the natural frequency of mixed robot, a variable stiffness model is proposed featuring the dependency of joint stiffness on the joint variables, rather than the constant joint stiffness in the traditional assumption. By integrating the variable joint stiffness model into a mode-reduced 4DOF model modified for the present study, the new method for predicting the robot natural frequency is then built, analyzed, and verified through simulation and modal tests by both a 3-axis accelerometer and a laser vibrometer on the milling robot under different robot configurations. Comparison of the experimental values from the modal tests against the natural frequencies predicted by the proposed model reveals a predicting error of less than 10%, hence enhanced accuracy of the proposed variable joint stiffness model in a large operational space. Based on the model, milling parameters without structural vibration has been selected, and the quality of the robot milling for titanium alloy has been improved.

Research on a Variable-Stiffness Joint and Its Application in Actuators

Variable-stiffness actuators can flexibly adjust the overall or local stiffness of a structure, thus enabling reconstruction, adaptation, and locking capabilities that can meet a wide range of task requirements. However, the programmable design and manufacture of three-dimensional (3D) variable-stiffness actuators has become a challenge. In this paper, we present a method to develop the 3D structure of variable-stiffness actuators that combines variable-stiffness joints with 3D printing technology. The variable-stiffness joints were obtained by arranging steel needles wrapped with enameled copper wire inside the grooves of a polylactic acid (PLA) structure and bonding the three components with silicone glue. First, a variable-stiffness joint was used as a variable-stiffness node and subjected to 3D printing to realize multiple 3D variable-stiffness designs and manufacture a programmable structure. Then, using the repulsive force between paired magnets, we developed a driving actuator for the 3D variable-stiffness structure, enabling the expansion and deployment functions of the structure. In addition, an electromagnetically driven mechanical gripper was designed based on variable-stiffness joints to effectively decrease the driving energy in applications where objects are held for extended periods using variable-stiffness control. Our study provides practical solutions and guidance for the development of 3D variable-stiffness actuators, contributing to the achievement of more innovative and practical actuators.

A 3D Printing‐Enabled Artificially Innervated Smart Soft Gripper with Variable Joint Stiffness

AbstractThe manufacturing industry has witnessed advancements in soft robotics, specifically in robotic grippers for handling fragile or irregular objects. However, challenges remain in balancing shape compliance, structural rigidity, weight, and sensor integration. To address these limitations, a 3D‐printed multimaterial gripper design is proposed. This approach utilizes a single, nearly fully automated 3D printing process to create a universal gripper with almost no assembly work. By processing functional polymer, polymer nanocomposite, and metal wire simultaneously, this technique enables multifunctionality. The gripper achieves different gripping configurations by adjusting joint stiffness through Joule heating of conductive polylactic acid material, ensuring shape conformance. Embedded metal wires, created using an in‐house wire embedding technique, form reliable high‐current‐loading interconnections for the conductive joints acting as the heater. Additionally, an integrated soft sensor printed in thermoplastic polyurethane (TPU) and conductive TPU detects compression levels and discerns handled samples. This study showcases the potential of 3D multimaterial printing for on‐demand fabrication of a smart universal gripper with variable stiffness and integrated sensors, benefiting the automation industry. Overall, this work presents an effective strategy for designing and fabricating integrated multifunctional structures using soft, rigid, and conductive materials, such as polymer, polymer nanocomposite, and metal through multimaterial 3D printing.

Разработка конструкции, моделирование и управление шарниром с переменной упругостью на основе магнитной пружины кручения

Разработка конструкции, моделирование и управление шарниром с переменной упругостью на основе магнитной пружины кручения

Robotic Modules for a Continuum Manipulator With Variable Stiffness Joints

Robotic Modules for a Continuum Manipulator With Variable Stiffness Joints

3D‐Printed Phase‐Change Artificial Muscles with Autonomous Vibration Control

AbstractCurrently, additive manufacturing is utilized to fabricate many different actuators suited for soft robots. However, an effective controller paradigm is essential to benefit from the advantages of soft robots in terms of power consumption, production costs, weight, and safety while operating near living systems. In this work, an artificial muscle is additively manufactured with soft silicone elastomer material capable of demonstrating several levels of stiffness. The 3D‐printed muscle is equipped with carbon fibers to receive a stimulus signal and develop a programmable joint that can present different stiffnesses. A nonlinear controller is developed to autonomously control the variable stiffness joint based on a reinforcement learning algorithm. The controller exhibits a slight increase in settling time; however, it demonstrates a decrease in fluctuation amplitude by 33% and a substantial reduction in power consumption by 41% in comparison to the optimized proportional integral derivative controller. At the same time, it is adaptable to and reliable in new conditions. The variable stiffness muscle is also used as a controllable mechanism to suppress the low frequency vibration. The study shows that the muscle can successfully attenuate the vibration autonomously when it is increased.

Tendon-Driven Gripper with Variable Stiffness Joint and Water-Cooled SMA Springs

In recent years, there has been an increase in the development of medical robots to enhance interventional MRI-guided therapies and operations. Magnetic resonance imaging (MRI) surgical robots are particularly attractive due to their ability to provide excellent soft-tissue contrast during these procedures. This paper describes a novel design for a tendon-driven gripper that utilizes four shape memory alloy (SMA) spring actuators and variable stiffness joints controlled by SMA coils for use in MRI surgical robot applications. The contact force of the gripper link is determined by the mechanical properties of the SMA spring actuators (SSA) and the angle of each linkage, and the joint stiffness can be adjusted by varying the electrical current applied to the SMA coil. To enhance the efficiency of the SSAs, a new cooling system using water has been proposed and implemented. To validate the effectiveness of our proposed gripper, we conducted three types of experiments, namely, a single SSA experiment, a single SMA coil experiment, and a whole gripper experiment. The experimental results demonstrate that the proposed water-cooling system can effectively solve temperature issues of SMA, and the joint stiffness in the austenite state is higher than that in the martensite state. Moreover, our experiments show that the presented gripper is capable of grasping and holding objects of various shapes and weights.

RJVS: A novel, compact and integrated rotating joint with variable stiffness

A variable stiffness joint is a key element for structural deformation, which is widely used in morphing mechanisms including mechanical arms, folding wings, etc. By adjusting the stiffness of the joint according to the external environment and/or system instruction, the motion response of the mechanical system can be controlled and its security and stability can be guaranteed. However, to develop a variable stiffness joint with small size and large bearing capacity is still challenging. Also, an accurate mathematical model and control method to describe the variable stiffness joint is very important. In this paper, a novel, compact and integrated rotating joint with variable stiffness is developed, whose rotational stiffness and motion can be real-time controlled. A new configuration of a stiffness-adjusting module with superior mechanical properties is proposed by changing the arm length of cantilever leaf springs. Then a universal mechanical model of stiffness which adapts to a wide range of deformation is proposed. The status of the stiffness-adjusting module is changed by rope driven in order to minize the structure. Angular displacement sensors and torque sensors are integrated to observe the static and dynamic performance of the joint. According to the established rotational stiffness model, the stiffness of the joint is adjusted by reverse calculation of the motor’s rotating angle. A nonlinear Proportion-Integral-Derivative method based on a Genetic Algorithm is proposed for motion control. The experimental results show that the proposed joint, with large bearing capacity and a wide range of stiffness adjustment, has integration functions of driving and sensing, and can achieve a good motion control performance.

An Anthropomorphic Robotic Finger With Innate Human-Finger-Like Biomechanical Advantages Part I: Design, Ligamentous Joint, and Extensor Mechanism

Exploring human hand fundamental biomechanical features and exploiting them to robotic hands have been proven to be an effective approach to enhancing artificial hands' performance, especially when interacting with various objects in dynamic unstructured environments. In this article, a bioinspired anthropomorphic robotic finger is first proposed, which embeds human finger musculoskeletal features in the design. Based on this design, three human-finger-like biomechanical advantages are systematically investigated and embodied in the bioinspired robotic finger. This article for the first time derives, presents, and experimentally verifies the mathematical models for the variable stiffness of finger ligamentous joints and self-adaptive morphing mechanism of finger flexible tendon sheaths, and validates and compares the influence of the reticular and linear extensor morphologies on fingertip feasible forces in three-dimensional (3-D) space. In this Part I of the article, two of the biomechanical properties, i.e., joint stiffness generated by the ligamentous joint of the finger, and fingertip feasible force space influenced by the reticular extensor mechanism are systematically investigated through theoretical modeling and experimental verification. Correspondingly, two biomechanical advantages were found, i.e., the ligamentous joint of the finger could provide anisotropic variable joint stiffness, enhancing the adaptivity, dexterity, and stability of fingers; and a reticular extensor mechanism could enlarge the fingertip feasible force space in 3-D space by 30.9% theoretically and 146.4% experimentally on average compared with the linear extensor, contributing to enrich force conditions during interactions. The third biomechanical advantage, i.e., fingertip force–velocity workspace can be augmented through the flexible tendon sheath, and grasping tests for a robotic hand designed with the aforementioned advantages are presented in Part II of this article.

Design and Analysis of a Novel Variable Stiffness Joint for Robot

The variable stiffness of robot joints plays an important role in improving the robot’s compliance, safety, and energy efficiency. In this paper, a novel type of variable stiffness joint based on a rack and pinion structure (VSJ-RP) is proposed. The structure and the variable stiffness principle of the joint are described in detail. The theoretical stiffness calculation and the dynamic model of the joint are established, and the correctness of the model is validated by simulation. The compliance, safety, energy storage, and release characteristics of the joint are validated by position, bearing capacity, hitting ball, and safety detection experiments, respectively. These experimental results show that the joint stiffness can be adjusted from 14.74 Nm/rad to 726.58 Nm/rad, and the overshoot of the position response is about 5.56–0.5%. The larger the stiffness of the joint, the faster the adjustment response, the smaller the fluctuation, and the more stable the operation are. The maximum output torque of the joint is about 20 Nm, and the torque difference between the minimum and the maximum stiffness of the joint is about 10%. The energy conversion efficiency of the joint is 17.56%~89.86%, and the deformation angle range is 2.66°~4.37°. These phenomena reflect the safety, energy storage, and release capacity of the joint. An effective exploration is performed regarding the miniaturization, safety, and energy utilization of robot variable stiffness joints.

Structural design and stiffness matching control of bionic variable stiffness joint for human–robot collaboration

The physical compliance of interaction is an important requirement for safe and efficient collaboration between robots and humans, and the realization of human–robot compliance requires robot joints with variable stiffness similar to those of human joints. In this study, based on the tissue structure and driving principle of the human arm muscle ligament, a robot joint with variable stiffness is designed, consisting of an elastic belt and serial elastic actuator in parallel. The variable stiffness of the joint is realized by adjusting the tension length of the elastic belt. Surface electromyography (sEMG) signals of the human arm are used as the characterization quantity of joint stiffness to establish the pseudo-stiffness model of the elbow joint. The stiffness of the robot joints is adjusted in real-time to match the human arm stiffness based on the changes in sEMG signals of the human arm during operation. Real-time compliant interaction of human–robot collaboration is realized based on an end stiffness matching strategy. Additionally, to verify the effectiveness of the human joint stiffness matching-based compliance control strategy, a human–robot cooperative lifting experiment was designed. The bionic variable stiffness joint shows good stiffness adjustment, and the human–robot joint stiffness matching strategy based on human sEMG signals can improve the effectiveness and comfort of human–robot collaboration.