# The Analysis of Mechanical Structure of a Robotic Leg in Running for Impact Mitigation
###### Abstract  
Legged robots suffer from the impact due to the consistent collisions with the ground. At the moment of collision, the sudden impact force not only causes the legs to lose contact off the ground, but can also reduce controllability and durability. This phenomenon becomes worse for the robots in running. In order to mitigate such an impact effectively, this study focuses on the mechanical structure of the legs, unlike the previous studies, which focused on the component level. The mechanical structures include actuator configuration, segment ratio, total length, and flexion direction. Contact inertia (CI), closely related to the impact, is derived and utilized to analyze the mechanical structure in terms of impact mitigation. A series of impact experiments with a fabricated leg verify that the mechanical structure affects mitigating the impact. impact; impulse; contact inertia; mechanical structure; running; legged robot Article  
The Analysis of Mechanical Structure of a Robotic Leg in Running for Impact Mitigation  
[PERSON], [PERSON], J.  
to the foot, to the leg, and then to the body, in that order. Fortunately, periarticular soft tissues and sponge-like cancellous (or trabecular) bones, located on both ends of the bone, attenuate the peak forces [16, 17]. Since legged robots structured mostly with rigid bodies are vulnerable to the peak forces in collision, however, the foot momentarily loses contact [18, 19], which would severely deteriorate the controllability of stance, as in Figure 1, showing our previous hopping experiment. In the hopping experiment, virtual compliance control was applied to the leg, but as soon as the tip of the leg touched the ground, a major collision occurred at the beginning, followed by a few minor collisions, as shown in Figure 1a. This phenomenon prevented the leg from being compressed enough to bounce back to the air. The virtual compliance was adjusted to mitigate the impact, but a similar phenomenon was repeated. The leg was even fractured after a few sets of experiments, as shown in Figure 1b. There have been dedicated efforts to attenuate such ground impact. Serial-elastic actuators (SEAs) were adopted in \"ANYmal\", developed by ETH [5], which gave mechanical compliance between the gearbox output and a joint [20, 21, 22], or springs were applied to the foot such that the robot could be adapted to dynamic interactions directly with the ground [23]. For \"MIT Cheetah II\", MIT pursued the \"massless\" concept ideal for impact mitigation with light legs and a low gear ratio. The legs featured the maximized strength-to-weight ratio through a tendon-bone mechanism inspired by biology [24]. Adding on to those light legs, the low gear ratio enabled high-bandwidth force control through direct contact without any medium such as mechanical compliance [25]. As previously mentioned, the current research on impact mitigation is limited to component-level approaches covering the mechanical components that make up the leg such as actuators, including the gearbox, linkages, and compliant mechanisms like springs and dampers. Therefore, the approach needs to be leveled up to cover the structural part of the leg. In order to mitigate the impact at landing of legged robots in running, this paper deals with a variety of mechanical structures such as actuator configuration, segment ratio, and overall length and flexion direction. First of all, the impulse at the point of contact is defined to quantify the impact. The impulse is expressed as the product of an impact velocity and contact inertia (CI), where CI is closely related to the mechanical structure, as well as the mechanical components. CI, which can be derived from dynamics, starts with single rigid body dynamics and then extends to the dynamics of articulating two rigid bodies that can represent a leg. CIs are compared by the mechanical structure listed above through simulations.