# Leg Trajectory Planning for Quadruped Robots with High-Speed Trot Gait
## 2 Materials and Methods
### Finite Element Analysis (FEA) of the Leg  
As mentioned above, there is a trade-off between the total leg weight and its strength. Therefore, in order to reduce the total weight and inertia of the leg without losing too much strength, the leg structure is mainly connected by ribbed plates with only 4-mm-thin plates in the middle, and the inclination angle of ribbed plates is 45 degrees to facilitate better performance of bearing pressure and bending moment. What is more, many thin-walled structures and lightweight materials were used in both motor and leg structure, which is likely to lead to insufficient strength and stiffness. Therefore, it is necessary to confirm the strength of the leg by Finite Element Analysis (FEA). During the locomotion of a quadruped robot, the leg movement mainly consists of two parts: a stance phase and a swing phase. The stance phase is a moment when the legs are stressed, and the weight of the robot body is supported by only two legs in the middle of the stance phase during trot and bound gaits. Considering that the quadruped robot needs to complete tasks like jumping over obstacles, which may generate an impact 2 to 3 times the weight of body [13], it is estimated that the total weight of the designed quadruped robot is \(\sim\)40 kg, so the maximum impact distributed to each leg is 1600 N. At the same time, the legs need to give the body a forward motion force, which was set to 1/10 of the impact (60 N). These two forces are applied to the endpoint of the leg model imported into Adams as load forces, and the forces generated in each part of the leg can be measured as shown in Figure 8.  
From the force analysis result, we know that each joint of the leg bears a large force under the ultimate load at the endpoint of the leg. In order to increase accuracy during the strength and stiffness checking, the forces obtained by the force analysis in Adams was further used as the load input for the deformation and stress analyses of each part by FEA with ANSYS software. The results are shown in Figure 9.  
Figure 7: Detailed design of the shoulder module. Figure 8: Force calculation by Adams. (**a**) Leg model imported in Adams. (**b**) Forces measured in each part of the leg. Figure 9: Cont. Figure 9: Finite Element Analysis (FEA): (**a**) The total deformation of the thigh; (**b**) the equivalent stress of the thigh; (**c**) the total deformation of the calf; (**d**) the equivalent stress of the calf; (**e**) the total deformation of the foot; (**f**) the equivalent stress of the foot; (**g**) the total deformation of the linkage  
connecting the knee motor and knee joint; (**h**) the equivalent stress of the linkage connecting the knee motor and knee joint; (**i**) the total deformation of the linkage connecting the thigh and foot; (**j**) the equivalent stress of the linkage connecting the thigh and foot; (**k**) the total deformation of the shoulder motor shaft; (**l**) the equivalent stress of the shoulder motor shaft; (**m**) the total deformation of the knee motor shaft; (**n**) the equivalent stress of the knee motor shaft; (**o**) the total deformation of the component connecting the thigh and the shoulder motor; and (**p**) the equivalent stress of the component connecting the thigh and the shoulder motor. It can be found that the maximum stress on each part of the leg is 245.6 Mpa, that is, less than 455 Mpa, which is the material strength of the 7075 aluminum alloy, and the structural strength of the leg meets the requirements with a high safety factor of 1.85. Also, there is a certain amount of deformation as a result of using a thin-walled structure and light aluminum alloy material resulting in lower stiffness brought about by the relatively lower weight of the leg. Moreover, from the view of natural animal running, the contact between their legs and the ground is a flexible contact rather than a rigid contact, which can decrease the peak force between feet and the ground and make the legs bear larger force.