本研究是針對雙足機器人在臨界狀態時腳與地面的反作用力，分別探討反作用力分布為單點力、線分布、與面分布三種情況，求出造成此臨界狀態的外力組合。本研究所針對的臨界狀態，主要是機器人在地面上滑動，但也探討機器人的傾倒。在線分布及面分布的情況皆是利用赫氏接觸理論，假設接觸區域內之應力為赫氏分布，並利用平面運動學中之瞬時中心原理求出臨界滑動狀態之切線應力。論文結果包括造成機器人滑動的力量(力矩)Fx，Fy，Mz的組合，以及可能造成傾倒之Mx，My的條件。 In this thesis we discuss ground reaction forces and moments on a foot of a biped robot under a critical stable condition. We treated the following three types of reaction force distribution on the foot: point force, line contact force, and area contact force, and determine force combinations to bring the foot into critical conditions. The emphasis of this study is on the critical stable condition of gross sliding, but the condition of falling is also discussed. We assume Hertz contact stress in line and area contact regions. The theory of instantaneous center of zero velocity in planar kinematics is utilized to determine tangential stress distribution. Results include all combinations of forces Fx, Fy, Mz to cause gross sliding and the possibility for moments Mx, My to cause falling.
