# Bioinspired Divide-and-Conquer Design Methodology for a Multifunctional Contour of a Curved Lever
## 1 Introduction  
Lever mechanisms have been used to amplify force or displacement for a mechanical advantage since time immemorial. Based on the conservation of energy, the amount of amplification a lever provides can be calculated as the ratio of the distance from the pivot point to the effort point and that from the pivot point to the load point. Numerous mechanical mechanisms and devices have been developed successfully with proper lever mechanisms [1, 2, 3, 4, 5, 6]. [PERSON] and [PERSON] proposed a torque generator-driven lever mechanism for a torsional mirror. In the mechanism, a lever was exploited to enlarge traveling distance in limited design space [1]. [PERSON] et al. developed a new design for a lever-propelled wheelchair [2]. [PERSON] and [PERSON] suggested a lever mechanism for improving vibration isolation performance. In their study, damping force was conveyed to the mass through the lever [3]. Several researchers have developed gripper mechanisms for microelectromechanical systems (MEMS) using lever mechanisms. [PERSON] et al. proposed a microgripper with a large magnification ratio. In this mechanism, the lever successfully amplified the limited output displacement of a lead zirconate titanate (PZT) actuator for the desired displacement of the gripper [4]. [PERSON] et al. developed a linear motor using a lever mechanism to improve the position accuracy. Unlike this mechanism of a microgripper, the lever mechanism in a linear motor had the role of reducing the displacement [5]. [PERSON] and [PERSON] developed a static balancing mechanism using a spring and lever. In this mechanism, the lever amplified the spring force and achieved a lightweight static balancer for a lamp [6]. In recent years, lever mechanisms with variable amplification ratios have frequently been applied in robot mechanisms, particularly variable stiffness actuators [7, 8, 9, 10, 11, 12]. [PERSON] et al. [7] and [PERSON] [8] et al. proposed adjustable stiffness actuators with class 1 levers for ankle assistance mechanisms. [PERSON] et al. [10], [PERSON] et al. [11] and [PERSON] et al. [12] also developed a class 1 lever-based actuator to achieve variable stiffness. To adjust the stiffness, the lever position was varied using an additional motor. [PERSON] andJ. [PERSON] also developed a variable stiffness actuator with a lever mechanism. When the class 2 lever mechanism was applied, the position of the lever's load point varied to change the actuator's stiffness [9]. Although the lever mechanisms with a variable amplification ratio achieved the desired function successfully, the shape for the levers was a straight line. Moreover, due to the simplicity of the straight lever, the above-mentioned studies did not propose a lever contour design methodology. However, when a lever had an additional required function beyond amplification such as preventing intervention between design spaces or maximizing the variable range of amplification ratio, the lever was required to have a shape other than a simple straight line. [PERSON] et al. developed a compact variable gravity compensation mechanism with a non-straight lever shape. An angled lever was devised to achieve the amplification of the spring force and also to satisfy the circular design space, [13]. [PERSON] and [PERSON] suggested an arc-shaped lever-based compliant actuator to satisfy both force amplification and energy-efficient stiffness variation functions [14]. Although these studies showed a non-straight lever shape, the geometries of the levers' contours were still simple and did not require any particular contour design methodology. [PERSON] et al. [15] proposed a curved lever design to improve the performance of a variable gravity compensation mechanism. In this method, the curved lever was mathematically modeled based on B-spline representation and optimized using a genetic algorithm. Although the research suggested a curved lever design methodology, there was a limitation that the lever contour was represented as a unitary curve.