A Novel Design of a Contractible, Tubular Continuum Manipulator

Continuum, maybe soft, manipulators or have strong capability in narrow space explorations and operations compared to the rigid links assembled robots. In this paper, we novelly designed a mechanism of continuum manipulator with contractible ability that gives the manipulator bigger workspace, more agile and flexible motion than those without contractible ability. Also, the proposed mechanism have big hollow inner space and light weight. The robotic system is composed of a continuum deforming structure, driving tendons with route parts, and an actuating module. We introduced the design of the mechanism and analyzed the workspace of a one-segment manipulator. Then, a prototype was setup to verify its motion ability.


INTRODUCTION
Continuum manipulators (CM) have good ability of obstacle avoidance and passive compliance which come from their flexible mechanism with a big length-todiameter ratio. They can serve in surgical operations, detection of aircraft or diesel engines, as well as some other operations with narrow spaces. [1][2][3][4][5][6] There are many types of the CM, which mainly include tendon-driven manipulator with flexible backbones [7,8], pneumatic arms composed of soft materials [9], concentric tube manipulator with very big length-to-diameter ratio [10], and snake-like robots with many independent severing motors-driven joints [11], etc.
We here focus on the CM with contract (extend) abilities. Reviewed the literatures, four types of contractible CM would be introduced as follows. (1). Pneumatic-driven CM. [9] They usually have soft-body structures that embed textiles or the differentiated wall thickness to constraint the undesired deformation. Moreover, researchers have developed a novel inflated manipulator that can grow its body even up to 70 meters. [12,13] The pneumatic-driven CM is powered by the pneumatic pressure so that they are often confused by the inadequate bending stiffness and difficult controllability. (2). Concentric tube CM [14][15][16]. These manipulators are composed of several very slim hyperplastic shape memory tube and form an extensible antenna-like structure. Each tube was mechanical programming bent, and the bending direction was controlled by their relative axial displacement and rotations. They can benefit to minimally invasive surgery with the follow-the-leader motions. (3). Magnetically extensible, tendon actuated continuum robot (METABot). [4,17] In this design, the magnetic disk is assembled by permanent magnets which can provide the repulsive force, and all of them can slide along with the central hyperelastic rod. (4) Mechanical spring-based tendon actuated CM. [18][19][20] Compared to the METABot, the repulsive force generated by the elastic potential energy of a compressed mechanical spring rather than that from the permanent magnets. Similar to the METABot, the mechanical spring-based tendon actuated CM eases the control complexities because it has better kinematics precision than pneumatic-driven CM and has a more agile workspace than the concentric tube CM. [20] In this paper, we designed a contractible CM based on a contractible mechanical spring. Different from the related work in literature [20], we designed a CM which is actuated by the wires rather than flexible rods. The bending stiffness of the wires can be neglected but that of the flexible rods used in work of [20] cannot be. More, the tendons continuously go through each turn of the spring rather than using separated links so that smaller curvature radius, bigger stiffness, and more smooth steering motion can be achieved, and the mechanical spring-based elastic skeleton enables the big hollow channel to transport like liquids, grippers, lasers, and cameras, etc. Also, our CM has 2 independent segments, causing better flexibility, more degrees of freedom, bigger workspace than that in [20]. The key contributions of this paper were listed as below: (1) Mechanical design of the robotic system, including the robotic body, actuating module, and control system. Mainly contribution of this paper is the design of the continuum mechanism of the robotic body. (2) Prototype and simple motion demonstration.

II. DESIGN OF THE ROBOTIC SYSTEM
The robotic body has 2 segments, each one was driven by 4 tendons. Sheaths of the tendons enable the remote driving ability of the robotic body, as well as the decoupling of the kinematics between the two segments. The tendon-driving mechanism is actuated by 8 reduced stepper motors (The stepper motor outputs torque of 0.05Nm with reducer ratio is 3.71), as Fig. 1 shows. For accuracy control of the tendons, as well as the compact design requirements of the mechanism, we choose a rolling mechanism to pull the tendons. The tendons were wound on the reel with slots so that the disorder of tendons can be avoided. The rotor that is connected to the stepper motor rotates the reel, meanwhile there is relative sliding movement between the reel and the rotor because of the internal thread inside the reel matched the fixed screw, then the tendon on the reel was pulling. To make the tendon has no translating skew, the reel should translate as the required speed. Here we use a fixed screw to provide the required translation (the reel has an internal thread acted as the nut to mate with the fixed screw). Fig. 2 is the prototype of the robotic system. The system composed by the robotics body, tendon-driven mechanism, motor driver and controller, and so on. It should be declared that the redundant 2 tendons was prepared for future work on stiffness variation research. Six tendons can actuated the robotics body adequately. Without payload consideration, the 2 redundant DoFs should be passively following the motion of the deforming robotic body required. Fig. 1 (a). The CAD model of the robotic system. Tendons and its sheaths of the segment 1 were not shown in this figure, which are similar to that of segment 2. Six motors are controlled to drive the tendons inside the robotics body. (b). Tendon-rolling mechanism. The rotor rotates the reel synchronously, and insider the reel there is internal thread that matched with a fixed screw, and the fixed screw gives the reel translation motion that guarantees the standing direction of the tendons. Fig. 2 The physical prototype of the robotic system. It compromised by the robotic body and tendon driven mechanism connected by the tendons (with sheaths), etc.

III. WORKSPACE ANALYSIS OF THE MANIPULATOR
In this section, we will analyze the workspace for the continuum manipulator with contractile ability compared to that without contractile ability. Some assumptions should be declared for the contractile manipulator in advance: The central-axis of every segment remains a circular curve in deforming; the minimum length of the manipulator determined by the wire-diameter d (in Fig. 3(a)) of the spring-like flexible skeleton, and one embedded length of the tendon can keep in maximum meanwhile the other embedded tendon has been in shortest (i.e., the state that of l1 = L0, l2 = lmin can be realized); the motion of the manipulator has geometric symmetry which makes its workspace is a rotational symmetric volume so that we can ease the problem into a planar model.
Upon the assumptions, the characteristic parameters of the circular curve, those are bending angle  and curvature radius  in Fig. 3(a), can be calculated according to the below analyses. The minimal length of the embedded tendon lmin = nd, where n is the turns of the flexible skeleton. The size parameters of our physical prototype were list in Table. 1. The geometry in Fig. 3(a) can yield that bending angle and curvature can be characterized as (1) The special situation of l1 = l2 was not taken into account here. The end-point E can be donated as (2)

Symbol
Value (mm) L0 The initial length of the embedded tendons of a one-segment manipulator The diameter of the wire-diameter 2 We use a generic ergodicity algorithm to scan the workspace of a one-segment contractile and uncontractile continuum manipulator, as Fig. 4 shows.
The additional constraint compared to that with contractile capability is that the centerline of the roboticbody should be kept constant in the length of L0 in the deforming process, i.e., lmin should be much more than nh, in this paper and l1+l2 = 2L0, we predefined that the maximal bending angle max = . (This is already an exaggerated contractile/extensile range according to the published works). The constraints were listed in (3) (3) From the above Fig. 4, we can know that the retractable ability enlarged the workspace significantly. The workspace of the former is a solid sphere-like with a small hole, but the latter is just a surface similar to that of a sphere. (Note that both of their workspace boundaries are not standard circular curves in cut view.) Here we simply show the motion flexibility and workspace in Fig. 4(a). It is declared that the motion of the robotic arm was controlled by a PS-2 gamepad, so there is no motion planning algorithm in this study. Besides, the contractile/extensive ability of the robotic arm is shown in Fig. 4(b).

IV. DISCUSSION
In this paper, we designed and test a novel continuum manipulator based on a contractile elastic spring-like skeleton. It exhibits advantages in the workspace that those continuum manipulators without contractile. With our mathematical model, a robotic arm with the required workspace can be analytically designed.
However, the workspace analysis in the current work is about that of a one-segment arm. This is mainly because that the ergodicity algorithm will cost too much computation time. Manipulators with two segments will reduce the gap of workspace between the manipulators with and without contractile ability, and we will study the workspace of the two-segment manipulator in the future.
Moreover, we did not test the trajectory tracking of the manipulator because we yet have not established the physical controller which is essential for how to actuate the motor timely. There is much engineering work to do in the future.
The payload ability of the proposed robotic arm, depending on the stiffness, should be discussed here. The payload can significantly influence the application range of the robot. This design makes its body softer in axisdirection than those manipulators with NiTi alloy skeleton or flexible rods instead of the tendons. However, the stiffness deeply depends on the materials and size parameters of the elastic skeleton. The design of the stiffness is also future work.