A Rigid Mechanism With Uniform, Variable Curvature1

Abstract

Slender, elastic, robotic manipulators can facilitate minimally invasive surgery (MIS) through nonlinear approaches to a surgical site, circumnavigating obstacles and vital organs. These so-called “continuum robots” have been developed using a variety of structural designs and actuation principles as reviewed in Ref. [1], e.g., tendon-actuated catheters, pneumatic colonoscopies, and concentric-tube steerable needles. However, the compliance that gives these manipulators their dexterity and range of motion also reduces their capacity for force application. Recent research has addressed these problems with new designs, such as the variable stiffness manipulator by Kim et al. [2], but current prototypes are still inferior to conventional rigid tools in their ability to exert external forces.In this technical brief, we propose a new tendon-driven mechanism consisting of a concatenated series of rigid-link, crossed, four-bar mechanisms that are mechanically constrained to produce uniform, variable curvature motion. The mechanism is unique in that it can conform to a curved path and withstand externally applied, high-magnitude forces without deforming. As a tool for MIS, it offers potentially improved performance for interaction with tough- or hard-tissues, such as those found in orthopedic procedures.A crossed four-bar mechanism with cross bars of equal length, L, and top and bottom bars of equal length, w, forms two triangles that share a side, x, as shown in Fig. 1. According to the side–side–side postulate, these two triangles are congruent and have equal angles. Two such mechanisms can be concatenated, sharing a common link (the top bar of one mechanism is the bottom bar of the subsequent one) in order to form a multi-degree-of-freedom (DOF) planar mechanism.Figure 2 shows that using an additional bar to link the corresponding crossed bars of two independent mechanism modules creates a secondary mechanism from the module-linking bar and sections of the primary mechanism. If the bar lengths of the secondary mechanism are geometrically similar to the primary mechanism, each primary module must exhibit the same angular deflection. If additional primary modules are further concatenated and constrained by module-linking bars, the chain will exhibit uniform curvature along its length as shown in Fig. 3. This reduces the mechanism to a single rotational DOF, α or θ, creating a rigid manipulator arm with actuatable curvature that follows the constant curvature kinematics described in Ref. [3].Connecting two such parallel mechanism chains at the top and bottom of each module (in essence, making a square tube from them) forms an arm or wrist with a large lumen that can be used as a passage for flexible surgical instruments to the end effector, which is useful for MIS. Any forces that are externally imposed on the manipulator will be transmitted through the concatenated mechanism, not the flexible instrument, and this will prevent unwanted deflection and allow for high force output at the end effector.Actuation tendons can be routed through the intermediate links that connect the two mechanism chains, allowing for a compact structure with actuators located off of the manipulator body. Additionally, a major advantage of this 1DOF design is that tendon tension is completely dedicated to resisting applied forces and not overcoming device elasticity—there is no build-up of tendon tension with increased tool curvature. In a multi-DOF design, several segments can be stacked in series with tendons routed through proximal sections.A small-scale prototype was created with machine screws and 3D-printed parts made from Taulman3D “n-vent” (Eastman Amphora™ 3D Polymer AM1800), as seen in Fig. 4. Two Kevlar thread tendons were routed through holes in the horizontal connection links (as shown in Fig. 4) and used to manually actuate the prototype from the end of a tube, demonstrating the use of this design as a wrist at the tip of an endoscope. The threa