本論文使用邊界元素法，探討在不同受力情況下機器人腳與地面之應力分布及接觸區域大小。外力Fx、Fy、Fz與力矩Mx、My、Mz可能造成雙足機器人行走時，在單足著地的情況下翻覆或者滑動的兩種不穩定狀態。其中Fz、Mx及My會影響腳與地面的接觸面積。其臨界情況是最後僅剩最後微小的接觸區域而即將產生翻覆；而Fx、Fy與 Mz則會產生腳掌在地面上局部滑動，其臨界情況是最後僅剩微小區域與地面附著，整隻腳的滑動即將發生。本研究針對以上兩種不穩定情況進行腳底的應力及接觸區域分析，並比較不同腳形以及將機器人腳模擬成剛體或彈性體的情況下之最大翻覆力矩，此外也比較邊界元素法與有限元素法結果的差異。 Boundary element method (BEM) is used to investigate the size of foot-to-ground contact region of a biped robot under various loading conditions, and determine stress distribution in the contact region. Applied forces Fx, Fy, Fz and moments Mx, My, Mz may cause a biped robot tip over or slide during the single-support phase. Among these forces and moments, Fz, Mx, and My determine the foot-to-ground contact size. The corresponding critical condition is the situation with a very small contact region, and the foot is about to tip over. On the other hand, Fx, Fy, Mz cause partial slip of the foot on the ground. The corresponding critical condition is the case with a very small region that has not yet slipped, which is close to the state of gross sliding. In this thesis these two possible types of instability are analyzed. Various shapes of robot foot have been dealt with. The foot may be rigid or elastic. Maximum allowable values for the moments are determined. The BEM results are compared to results obtained by finite element analysis.
