Kinematic/static performance evaluation and geometric parameter design of parallel-driving leg mechanism

Abstract: In order to raise mechanization and automation level of agricultural operations, broaden the scope of application of agricultural robot, a novel three degree of freedom leg mechanism used in the six-legged walking robot was introduced. The kinematic and static performances of the leg mechanism were analyzed. The geometric parameters of the leg mechanism were optimized by multiple objectives. In this paper, firstly, the coupling relationship between the linear velocity and angular velocity of the foot was resolved. The kinematic performance index was defined based on the condition number of Jacobian matrix. The distribution diagram of kinematic performance index was drawn. It can be seen that kinematic performance index was small in the central area of workspace of the leg mechanism from this distribution diagram. It was shown that the kinematic performance of leg mechanism was better in the central area than other areas of workspace of the leg mechanism. Secondly, the ground surface types were summarized as hard and soft ground surfaces considering the acting generalized force types between the standing foot and the ground surface. The acting generalized forces were three-dimensional pure force when the ground surface type was hard ground. The acting generalized forces were six-dimensional force when the ground surface type was soft ground. The driving static model of the whole leg mechanism was built based on the principle of virtual work. Then according to different ground surface, the local and global static performance evaluation indices were proposed. The distribution diagrams of the local static performance evaluation indices were drawn, respectively. It can be seen that the load performance was batter in the area of y>0 than the one in the area of y<0 (as shown in Fig.1). Again the closer to the boundary of workspace the leg was, the better the static transfer performance of the leg mechanism was. But, the leg mechanism needed more rough ground to provide enough friction when the standing leg was in the boundary of its workspace. The constraint Jacobian matrix of the driving mechanism was built based on the theory of linear space. The constraint statics performance evaluation indices were proposed based on constraint Jacobian matrix. The distribution diagram of the local constraint statics performance index was drawn. From the distribution diagram, it can be seen that constraint force transfer performance index remained unchanged in everywhere of the workspace and constraint torque transfer performance index was smaller in the area of x=0 than other areas. It was shown that constraint force transfer performance of driving mechanism was good and constant in whole workspace, constraint torque transfer performance of driving mechanism was better in the area of x=0. Lastly, aiming at improving comprehensive property of leg mechanism, its geometric parameters were optimized using searching method. Optimization results showed that when the parameters of the long rod and connecting rod of parallelogram mechanism was 330 mm and 140 mm, respectively, the parameters of rod connected with ground was 320 mm, comprehensive property of leg mechanism was better. Compared with before optimization, the kinematic performance of the optimized leg mechanism was increased by 5.46%, the maximum gravity load was increased by 18.02%, and the maximum torque of the driving joint was reduced by 6.33%. The hexapod robot was designed based on optimized parameters. The research results provide a theoretical basis for the gait planning and control of the six legged robot. Meanwhile, optimal design method for geometric parameters of leg mechanism of the six-legged robot applied in this paper is also applicable to other six legged robot.