【摘要】 针对连杆曲线形态特征随机构尺度变化的复杂性,借助平面运动几何学、拓扑学相关理论,提出了基于连杆曲线奇点的形态学分析方法。利用现代几何学曲线曲率理论,构建了尖点、二重点和自切点的数学方程,依据平面四杆机构运动的几何约束关系,解算奇点存在的约束方程,分析了尖点、二重点和自切点的渐变特性,实现了对连杆曲线奇点间相对拓扑关系和位置信息的数学描述,获得了连杆曲线的奇点拓扑环。该方法不仅加深了对连杆曲线尺度变化规律的理解和认识,并且可为对连杆曲线突变和渐变宏观规律的快速判断与掌握提供理论依据。更多还原

【Abstract】 Aiming at the complexity of scale change of morphological characteristics of connecting rod curve,the method of morphological analysis based on the singularity of connecting rod curve is proposed by means of plane motion geometry and topological correlation theory. Using modern geometric curve curvature theory,the sharp point、two-point and self-tangent point mathematical equations were established. Based on the geometric constraint relations of plane four-bar mechanism,the constraint equations of singular points are solved. According to the sharp point、two-point and self-tangent point of the scale change characteristics,the mathematical description of relative topological relation and position information between singular points of connecting rod curve is realized. The singular point topological ring of the connecting rod curve is obtained. This method not only deepens the understanding and understanding of the law of scale change of connecting rod curve,but also provides a theoretical basis for rapid judgment and mastery of sudden change and gradual macroscopic law of connecting rod curve.更多还原