Abstract

The Darboux mechanism is considered. It is proved that this hinge mechanism allows the rotational movement of one link to be converted into (strictly) straight linear movement of its top H. The links of the Darboux mechanism can form geometric shapes such as triangles and squares (with diagonals drawn). In the “square”-shaped configuration of the mechanism, geometrically, branching may occur when the vertex H can move both along a straight line L and along a curve γ. In this case, the rank of the holonomic constraints of the system diminishes by one. For direct linear motion of the vertex H, the Lagrange equation of the second kind in terms of the point H coordinates is derived. The coefficients of this equation can be smoothly continued through a branching point. The “limiting” behavior of the reaction forces in the rods is studied when the mechanism moves to the branching point. An external force that does not do work on point H leads to unlimited reactions in the rods. The kinematics at the branching point is also studied. The inverse problem of dynamics at the point where the rank of the holonomic constraints is not a maximum is solvable. The Lagrange multipliers Λ_i at the branching point are not defined in a unique way, but the corresponding forces acting on the mechanism vertices are uniquely defined.

中文翻译：

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达布机构直线运动动力学的具体特征

摘要

考虑达布机制。事实证明，这种铰链机构可以将一个连杆的旋转运动转换为其顶部H的（严格）直线运动。达布机构的连杆可以形成三角形和正方形（画有对角线）等几何形状。在该机构的“方形”形状配置中，几何上，当顶点H既可以沿着直线L移动又可以沿着曲线γ移动时，可能会出现分支。在这种情况下，系统的完整约束的等级减一。对于顶点H的直接直线运动，推导了以点H坐标表示的第二类拉格朗日方程。该方程的系数可以平滑地继续通过分支点。当机构移动到分支点时，研究了杆中反作用力的“限制”行为。不对H点做功的外力会导致杆中产生无限的反作用力。还研究了分支点处的运动学。当完整约束的秩不是最大值时，动力学反问题是可解的。分支点处的拉格朗日乘数Λ _i没有以唯一的方式定义，但是作用在机构顶点上的相应力是唯一定义的。