# Design and Analysis of a Planar Six-Bar Crank-Driven Leg Mechanism for Walking Robots
## 1 Introduction  
In recent times, the growing integration of robots into daily life has emerged as a fascinating field for research and development. This growth has prompted many to focus on enhancing automated machines for various purposes. Over the years, advancements in science and technology have transformed robotics from a concept of fiction into a tangible reality, especially in terms of robot design and manufacturing. Various disciplines, including computer science, medical applications, engineering, and automation, have significantly contributed to the progress made in robotics [1; 2; 3]. A walking machine is characterized by its ability to move over soft or hard surfaces using limbs, legs, and/or wheels at low speeds. NASA has extensively researched the design and development of these machines for planetary exploration since the 1960s [1]. Depending on the terrain, NASA has developed three primary types of walking machines: wheeled, tracked, and legged robots. These versatile machines are utilized in various fields, including planetary exploration, medical applications, engineering, and agriculture, to enhance or substitute human efforts [4; 5; 6]. Among the diverse leg mechanisms utilized in walking machines, the Klann mechanism and Jansen's linkage stand out for their widespread application. The Klann mechanism [7; 8; 9], a pivotal example of an eight-bar kinematic chain, replicates the locomotion of legged animals and serves as an alternative to traditional wheels. It comprises a frame, cranks, a pair of grounded rockers, and two couplers connected by pivot joints. This design offers notable benefits for walking machines, such as the ability to move over obstacles like curbs and stairs and access areas challenging for wheeled mechanisms without the need for sophisticated control systems or extensive actuation devices. In their research paper, [PERSON] et al. [9] designed and modeled a paired four-legged amphibious robot capable of walking on land and swimming in water. They utilized an optimized Klann linkage mechanism for the robot's legs. Their kinematic analysis and inverse dynamic analysis, conducted using a SAM (Simulation and Analysis of Mechanisms), confirmed that the Klann mechanism provided a horizontal foot trajectory, resulting in higher propulsion compared to a four-bar mechanism. The study demonstrated the robot's capability to maneuver effectively on different surfaces. The Klann mechanism was found to be more efficient and provided better propulsion and speed performance. The Jansen linkage [7; 8; 9; 10], renowned for its ability to produce a fluid walking motion, ingeniously transforms a simple rotational input into a lifelike stepping pattern. This mechanism, characterized by its single degree of freedom (DOF) and an eleven-link leg configuration, adeptly converts the circular motion of a crank into the linear gait of a walk. Its design is both scalable and energy-efficient, offering a low payload capacity while ensuring a predictable path for each footstep. The key advantages of the Jansen mechanism are its simplicity and effectiveness, making it a preferred choice for implementing walking motions in the field of legged robotics. Recently, [PERSON] et al. [11] introduced the development of a novel closed-chain elastic-bionic leg (CEL) mechanism, which incorporates a single actuated DOF inspired by the spring-loaded inverted pendulum (SLIP) model. This innovation aims to improve the efficiency of leg mechanisms in robotic applications, focusing on simple control, enhanced stiffness, and the capability for full rotation driving. The design features an eight-bar linkage that mimics the muscular and skeletal structure of a cheetah's leg, targeting optimal performance in high-speed conditions. By employing a kinematic analysis, their study establishes a link between foot trajectory, ground reaction forces, and driving forces, further examining the stiffness changes in the support phase using an equivalence model.