采用变长梁单元的柔性平面连杆机构的KED分析

本文采用变长梁单元来处理机构中的所谓“导杆”构件,在弹性小变形范围内,导出了考虑弯曲、剪切及轴向三种变形型式和计及截面转动惯量、端点集中质量、纵向弯曲影响的柔性平面连杆机构系统最一般的弹性运动微分方程式,不仅使其与全转动副柔性平面连杆机构KED分析在形式上得到了完全统一,而且更简明地给出了求其稳态解的Four柏r级数系数方程式.作为算例,文中给出了一转动导杆机构相应数值计算结果.

A Kineto-Elastodynamic Analysis of Planar Linkage Mechanism Using Variable-Length Finite Beam Elements

The KED analysis for a planar flexible linkage mechanism with moving prismatic pairs between movable links is difficult if it is made by means of constant-length beam elements alone. Variable-length beam elements are therefore used to deal with the so-calleed "guipe" links. Under the assumption of small elastic deformation, general elastic motion equations for a planar flexible linkage are derived, in which the axial, bending and shearing deformations, the influence of moment of inertia, the concentrated mass at both ends and the effects of longitudinal tensile loads on the elements have been taken into consideration. The equations are identical in form as those for a planar flexible linkage only with revolute pairs.When the periodicity of the steady motion of the planar linkage mechanism and the orthogonality of trigonometric functions are used to handle the integral of the equations in a period, the relational equations of coefficients of Fourier series of steady-state solution are found to be simpler and clearer. A numerical example is given.