Design method for a bionic wrist based on tensegrity structures

The traditional bionic upper limb structure design is limited by the motion pair and cannot guarantee the flexibility of the mechanical structure. The tensegrity structure has the characteristics of high deformability, strong self-adaptability, and resistance to multi-directional impact. According to the biological characteristics of the upper limbs of the human body, an anatomical study is performed on the upper limb wrist joints that achieve adduction/abduction, flexion/extension, to obtain the relationship between the movements of the related bones and muscles, and to simplify the shape and structure of the wrist. Equivalent mapping of a mechanical model based on two-bar tensile properties. Through the contraction and stretching of the spring, the movement characteristics of the human muscles are realised, and the optimised bionic upper limb wrist tensioning robot without motion pair is further obtained. Adams simulation is used to verify that the bionic tensile wrist can simulate the change movement of the human wrist. The experimental platform was built and a physical prototype was made and the prototype was tested. The results show that the bionic tensile wrist can realise the adaptive motion characteristics of the human wrist well and stably, which proves the validity and feasibility of this design method.


Introduction
Conventional manipulators mostly use rigid structures and use ball pairs to achieve the function of the wrist. Due to the mutual balance mechanism, the manipulator is heavy and the steerability is usually limited. The existing dual-arm manipulator usually consists of two six-degrees-of-freedom (6-DOF) or 7-DOF arms, the number of which is equal, resulting in the mechanism of the manipulator becomes no longer compact and the length increases, inertia and weight also increase, so more power is needed to drive the mechanism [1][2][3][4]. Bionic robots emerge as the times require, but the traditional method of designing anthropomorphic robotic hands usually involves mechanised biological components such as hinges [5], connecting rods and universal joints to simplify complex bionic movements. Most of the joints of bionic robots can be simplified into the form of spherical joints. Artificial joints are now widely served as a treatment to joint diseases such as osteoarthritis. Different bearing material combinations have been used in making artificial joints [6]. However, the current artificial joints are mostly metal materials, larger volume, heavy mass. The spherical 3-DOF parallel manipulator proposed by Richard [7] can make the manipulator grab the object from different angles. Liu et al. [8] proposed a series-parallel 7-DOF redundant anthropomorphic arm whose spherical 3-DOF parallel mechanism was used as the design of the shoulder and wrist. However, under certain extreme conditions, such as when colliding with a hard object, the structure of the spherical joint is easily damaged because there is no translation motion in the radius direction to reduce and absorb the energy of the collision.
Compared with traditional bionic robots, soft robots have a wider range of application space. It has a softer structure, is adaptable to the environment, and can adapt to different needs by changing its physical structure under certain conditions. Tensegrity robots because their tension mesh distributes the applied force more evenly throughout the structure, so it can resist the impact of forces in all directions. Therefore, even a light robot can withstand relatively large impacts and loads [9][10][11][12][13].
With the increase in the study of the tensegrity structures, which the demand is increasing, because these structures can well imitated the specific joints in the human body. Based on Scarr's passive elbow design [14], Turvey and Fonseca proposed the necessity of establishing and studying the entire joint of the elbow tension. The elbows are treated as a mechanism that conforms to the principle of tensegrity structures, and the rods (compression elements) are held by ropes (tension elements). The compression element is designed to mimic the bone, and the tension element mimics the muscles and fascia [9]. Although this design pattern does not strictly focus on anatomical accuracy, it shows that the basic hinges in traditional elbow designs can be designed with the tensegrity structures. However, the research on the adaptive movement of the human wrist using the tensegrity structures has not gone to report. In daily life, rotating behaviour represents the contact between a static finger and a rotating device [15]. As an important hub connecting the hand and arm, the rotating movement of the wrist is not just the function of the wrist, so this study does not cover an overview of the rotational motion. In this paper, the tensegrity structures are applied to the design of the humanoid upper limb forearm robot. According to the motion mechanism and morphological structure of the human wrist, the bionic mechanical forearm wrist joint is established through the bionic mapping, which has the characteristics of good self-adaptability of the motor function and can simulate the adaptive movement characteristics of the human wrist. Based on the characteristics of passive driving, according to the external motion requirement the self-spring deformation is utilised, so that the mechanism passively makes the movement demand of the angular range adjustment of the adaptive motion, thereby achieving the goal of adaptive motion.
to adapt to the action of complex movements. The wrist joint consists of eight bones, they are: (1) scaphoid bone, (2) lunate bone, (3) triquetral bone, (4) pisiform bone, (5) trapezium bone, (6) trapezoid bone, (7) capitate bone and (8) hamate bone. Muscles are composed of the muscle belly and tendons, which are coupled to the bones by the tendons, use the muscles to contract to create a tensile load, transmit the tensile load to the bones through the tendons and pull the bones to produce motion. At the same time, the radial carpal ligament is a biological tissue that connects bone to bone, providing a major guide to prevent bone rotation and ensure joint interaction through the range of activity, thus maintaining the stability of the wrist bone. The ligament connects the ulnar humerus of the forearm to the carpal bone and connects the carpal bones together. The contraction of the muscles, especially the contraction of the flexors, maintains the wrist complex. The wrist joint is a typical elliptical joint that moves around two axes. When the hand is made before and after, swinging the movement left and right, the stretching function based on the ligament of the ligament restores the wrist joint to its original position and is stabilised. Through the dynamic deformation of the radiocarpal joint and the midcarpal joint, the wrist is adjusted to a certain extent to ensure the realisation of the wrist action function. Thereby, the upper limb forearm achieves adduction/abduction, flexion/extension motion through the wrist joint Fig. 1.

Bionic design based on tensegrity structures
The wrist of the human body has a special movement and action mechanism, which enables the upper limbs of the human body to adapt to the action of complex movements. The human wrist is not a single-moving structure that includes bones, muscles, interosseous ligaments, and cartilage tissue. Researchers such as Viceconti simplify the body as a musculoskeletal biological system, and discontinuous bones use continuous muscle ligament coupling to maintain the stability of the human body [16]. Pandy Marcus and Thomas [17] introduced the unique role of human muscles in the exercise mechanism.
A schematic diagram of the musculoskeletal ligament system of the wrist is shown in Fig. 2a. In Fig. 2a, yellow and green respectively represent the eight bones of the middle wrist joint, namely, (1) scaphoid bone, (2) lunate bone, (3) triquetral bone, (4) pisiform bone, (5) trapezium bone, (6) trapezoid bone, (7) capitate bone and (8) hamate bone, and red represents muscle bundle and ligament tissue. According to the musculoskeletal biocoupling characteristics of the wrist, the movement pattern of the wrist joint is extracted by analysing the movement mechanism of the wrist, and the wrist muscle group is simplified, as shown in Fig. 2b. The flexor carpi ulnaris and musculi flexor earpi radialis, the palmaris longus realises the flexion movement of the wrist joint, the extensor carpi ulnaris and extensor carpi radialis longus, and the extensor carpi radialis brevis realise extension motion of wrist joint; Similarly, flexor carpi ulnaris, extensor carpi ulnaris, flexor carpi radialis, extensor palmaris longus and extensor carpi radialis realise the adduction and abduction of wrist joint, respectively. It provides a design method for the theoretical study of the bionic tension wrist mechanism. The wrist is a complex joint with two consecutive joints, namely the radiocarpal joints and the midcarpal joints [18,19].
As shown in Fig. 2, according to Gray, the hand flexion is the result of the joint action of six muscles. The cubitalis gracilis is located in the anterior part of the forearm, and the musculi flexor earpi intersecting diagonally at the anterior end of the forearm obliquely passes through the anterior part of the forearm and is attached by the main tendon. Long and thin tendons and aponeurosis palmaris assist wrist joint in flexion. The cubitalis anterior is located in the anterior part of the medial forearm, which is helpful for wrist flexing and adduction. Superficial platysma and unguiflexor digitorum move along humerus, ulna and radius, and are responsible for bending wrist and two fingers. The biceps femoris, located in the middle of the brachioradialis, is mainly responsible for wrist joint extension and abduction. Flexor carpi radialis is a long muscle that originates from brachialis and is attached to the base of finger. It is helpful for radial deviation of musculi extensor carpi radialis brevis, also known as abduction. Flexor carpal muscle is a long muscle, originated from humerus and ulna, and realises adduction of wrist joint together with carpal   Fig. 2c, based on the characteristics of the biological coupling between the wrist muscles and bones, the cubitalis anterior and the flexor carpi radialis are simplified, and cubitalis gracilis is a bundle of muscles to realise the flexion movement of the wrist joint. Cubitalis anterior, musculi extensor carpi radialis longus, and musculi extensor carpi radialis brevis is a bundle of muscles to achieve straightening of the wrist joint; In the same way, the cubitalis anterior and cubitalis posterior, flexor carpi radialis, cubitalis gracilis and extensor radials muscle are simplified. Then, we realise adduction and abduction of the wrist. During the abduction, the scaphoid bone rotates around the horizontal axis. To connect with the radius, the proximal articular surface of the wrist joint moves outward from the joint capsule. The proximal and distal ends of the wrist are bridged by the scaphoid bone, providing functional coupling between proximal and distal ends. Based on the coordinated action of the interosseous ligaments of the wrist, the dominant muscles and ligaments in the wrist joint are extracted to optimise the organic combination between the bones and ligaments of the wrist [20,21]. Wrist relationship diagram is shown in Fig. 2d.
It is well known that the human wrist bone is not a fixed structure. Under the condition of mutual contact between the bones and ligament constraints, the relative motion generated between the carpal bones will change the shape of the carpal bone. Therefore, we suspect that the musculoskeletal system of the human wrist may be a complex tensegrity structure, which uses a flexible muscle ligament and rigid bone to form a stable self-balancing structure with good adaptability. According to the morphological structure of the wrist, the structure of the upper limb forearm forms a spatially staggered structure with tensegrity properties, and the structure is shown in Fig. 2d. According to the structure, organisation and function of human wrist joint, elastic components  were used to simulate the biological characteristics of the outer muscle and ligament of the wrist by the principle of similarity, the biological characteristics of bone are simulated by rigid components and the stability of the structure is realised by replacing the bone tissue with additional rigid components. According to the configuration characteristics of the structure space interlacing and two-bar tensioning proposed by Snelson [22], as shown in Fig. 2e, combines with the theoretical knowledge and design method of the mechanism, the motion of the mechanism is realised by using the rotating pair connection. The position of the centre of gravity of the mechanism utilises the rigid member to connect with the frame through the x-axis motion of the universal joint and realise the buckling and straightening motion of the mechanism; Through the y-axis movement of the universal joint and two-bar tensioning, the mechanism's adduction and abduction movement is realised, and the movement characteristics of the mechanism are completely expressed. According to the position and relationship of the wrist bones, the tensegrity structures of the bionic tension wrist are designed. The mechanism diagram is shown in Fig. 2f.

Discussion and simulation
The existing bionic wrist robots do not conform to the anatomy of human physiological structure. They are heavy and inflexible. Moreover, they are not easy to control, and their stability is unknown. The disadvantage of the motion of some wrist robots, which is driven by air, and it is not easy to control. The pneumatic way to drive the limb has achieved a certain degree of success. However, due to the complex design, the flexibility and cost of the wrist joint cannot be highlighted. At present, it can control well and is simple to make by rope drive. Some soft robots, however, such as those which adhere to the principles of tensegrity, are typically better able to flex under stress and absorb impacts from many directions [13,23]. Therefore, in this paper, the main idea is proposed, which is to use the rope drive to realise the movement function of the wrist joint based on the principle of the tensegrity structures.
Compared with the traditional robot wrist mechanical device, the biologically inspired wrist mechanism proposed in this paper is relatively simple and lightweight. The carpal bones are divided into articulations radiocarpea and midcarpal joints for discussion based on anatomy in the study of this thesis.
It is better than the traditional mechanism that studies the wrist joint as a whole. We proposed to divide the wrist joint into two parts to study, which is more suitable for the physiological structure of the human body. As shown in Fig. 3, O is the state diagram of the mechanism after adding constraints and driving in Adams. ABCD correspond to the corresponding wrist action diagrams, and the results can be clearly seen. The four springs connecting the semicircle and the crossbar represent the articulations radiocarpea, and the lower two-bar three-spring tension bodies represent the midcarpal joints. By driving the motion pair, the mechanism can obtain the deformation and angle of each spring when making various actions. The relationship curve is shown in Fig. 4. For a robot based on the tensegrity structures, this proves the corresponding relationship between the bionic tension mechanism of the wrist and the physiology of the human body. A prototype is made and built the experiment table. The mechanism is controlled by a rope to achieve similar human body wrist movement changes, as shown in Fig. 5. At the same time, adding carden joint to our structure makes the mechanism more stable. Through the current adjustment, the structure of the mechanism is simple design, good flexibility, low cost, small size, lightweight, and has better adaptability than the traditional wrist mechanism.
In this part, the ADAMS software is used to simulate the kinematics simulation of the virtual prototype model of the bionic upper limb forearm wrist joint to determine the position and speed of the system and its various components at any time. The simulation results show that the bionic model can realise the change movement similar to the human wrist and observe the whole process of the spring changing with the angle. As shown in Fig. 3. According to the physical properties of human tissues, aluminium materials are used in rigid structure and springs are used in the elastic component. The rigid members are lightweight and the elastic members meet the structural requirements. The simulation start and stop time is set to 5 s, the step length is 1000, the adduction/abduction movement speed and the rotational speed are 1 mm/s and 6°/s, respectively, and the flexion/extension movement speed and the rotational speed are 1 mm/s and 10°/s, respectively. The relationship between the spring shape variable and the angle is given. As shown in Fig. 4, Spring x (x = 1, 2, 3, 4, 5, 6, 7) represents a simulation result graph of the x-deformation of the corresponding motion state spring. The simulation results show that the bionic wrist mechanism can passively realise the changing motion of the human wrist.

Physical prototype manufacturing
According to the size characteristics of the physical model, the physical prototype is fabricated using 3D technology (in Fig. 6). The main parameters of the physical prototype are shown in Table 1.
In Fig. 5, the motor drives the roller to make the ropes l 1 and l 2 wound around it. The ropes are considered to pass through the corresponding positions, the windings and fixing methods of the ropes are determined, and the experimental prototype is made to drive the two rods g 1 and g 2 on the prototype and move synchronously.
The prototype is in good working condition so that the adduction and abduction movements of the wrist are realised. In the same way, the second drive realises the flexion and extension of the mechanism. Fig. 5 shows a physical prototype of a bionic upper limb forearm wrist joint. The compression element is driven by a 3D printer, and the tensile element is composed of a lightweight small spring. To facilitate the observation and effect of the experiment, use the three springs at the lower end with a more elastic rubber band, and the driving tensioning element is made of a fishing line. To realise the action function of the bionic wrist joint, programmed a controller controlled by a computer that uses a small motor combined with a reel to shorten and elongate the part.

Conclusion
In the past few decades, with the development of new materials chemistry and processing technology, biomaterials have evolved from static and inert to dynamic and intelligent. Various biomaterials are used in the joint surfaces of artificial joints. Friction on joint surfaces and the connection between modular components and bones are important considerations. Biotribology studies the application of tribology principles in medicine and biological systems, such as friction, wear and lubrication between relatively moving surfaces. For example, stair climbing may double wear in a knee implant, compared with level walking. The cartilage that covers the end of the knee bone is a wear-resistant material. Synovial membranes reduce friction during joint motion. The function of the wrist joint is similar to the universal joint, which can bend and stretch when carrying the load from ulna radius to hand during normal grasping of the human upper limb, and at the same time bear certain wear. The synovium plays a role in lubricating joints. Therefore, the biotribology involved in the wrist joint, to reduce friction as much as possible, to maximise the realisation of human physiological functions is what we need to consider in the future.
Focusing next on the human arm muscles, the arm driving scheme consists of numerous muscles working in pairs with redundant pairs of muscle to serve as stabilisers. These pairs of muscles are also arranged in a closed-loop fashion, similar to that of parallel mechanisms. Human muscle physiology is also observed to be of similar characteristics with cables (both having the unilateral property of only being able to pull), while they are also flexible. Because joint torque of the musculoskeletal system for movement is generated by the imbalance between tensions of agonist and antagonist muscles which have inherently spring-like properties, stiffness during movement is an important factor in the study of the biological motion control mechanism. Because of the spring-like properties of muscles and reflex loops. As asserted by Bizzi et al. (1992) and Feldman and Levin (1995), we believe that the inherent spring-like properties are beneficial not only in controlling posture but also in reducing the complexities involved in controlling novel multi-joint movements.
As discussed above, the elastic element herein is composed of a spring, these springs present a non-linear characteristic which is closer to the behaviour of the human articulations with regards to linear springs. In addition, these low-cost elastomeric components present a high torque/thickness ratio which is a very important feature for developing miniaturised devices. However, in other applications, where the hysteresis of the polymeric material is an issue, it would be possible to replace the elastomeric spring with traditional metal springs. As the acquisition of knowledge as to how to regulate many muscles for the required movements proceeds, the fatigueless movement with low stiffness could become progressively dominant [24][25][26].
In this paper, a design model and method of bionic upper limb forearm wrist joint based on tensegrity structures are presented. The main advantage of the proposed design is that the tensegrity structures may be more flexible than conventional rigid robots, which can alleviate more uncertainty and have better adaptability than fully flexible robots. Subsequently, the simulation test showed that the bionic tension wrist joint achieved a movement similar to the wrist of the human body. In the simulation analysis, the range of motion of the mechanism's in-and-out abduction is (0°-45°) and (0°-15°), and the range of motion of the flexion straightening is (0°-85°). At the same time, the experiment also shows that the physical prototype can better achieve the movement similar to the human wrist and has good self-adaptability.
The tensegrity structure is a new application in the field of mechanical design and robotics. Its main disadvantage is that it needs advanced control technology to carry out drive design. However, its movement flexibility and structural adaptability are unmatched by other structures, so it provides a more novel theoretical basis and design concept for the future upper limb physical therapy and human prosthetic field.

Acknowledgments
This study was supported by the National Natural Science Foundation of China (grant no. 51875047) and by the Science and Technology Development Planning Project of Jilin Province of China (grant no. 20170101213JC). The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.