按许用传动角综合曲柄摇杆机构的非迭代法

建立了按许用传动角γ]综合Ⅰ,Ⅱ型平面曲柄摇杆机构的一元四次方程。已知极位夹角θ、摇杆摆角ψ时,按γ]综合Ⅰ型机构(ψ≠θ时)及Ⅱ型机构的统一方程是以曲柄相对尺度a为未知量的全系数一元四次方程;而按γ]综合特殊Ⅰ型机构(ψ=θ时)的方程是以连杆相对尺度b为未知量的简单一元四次方程。基于实系数一元四次方程的矩阵解法,提出了按γ]综合Ⅰ型机构(ψ≠θ时)及Ⅱ型机构的统一非迭代算法。给出了综合实例,并对求解结果进行验证。实例表明非迭代算法简便、快速、精确。

Non-iterative method for synthesizing the crank-rocker mechanism according to allowable transmission angle

The unary quartic equation of Ⅰ, Ⅱ typed planar crank-rocker mechanism synthesized in the light of allowable trans-mission angleγ] was established.While the included angle θ be-tween extreme positions and the rocker swinging angle ψ were known, the unified equation for synthesizing the type I mechanism (whenψ≠θ) and type Ⅱ mechanism according to γ] was a com-plete coefficients unary quartie equation that takes the crank relative dimension a as the unknown.But the equation for synthesizing the particular I typed mechanism (when ψ =θ) according toγ] was a simple unary quartic equation that takes the connecting bar relative dimension b as the unknown.Based on the matrix solving method of the real coefficients unary quartic equation, the unified non-iterative algorithm for synthesizing type I mechanism (when ψ≠θ) and type Ⅱ mechanism according to γ] was put forward.A synthetic living example was presented and verification was carded through on the result of solution.This living example showed that the non-iterative method is rapid, accurate, simple and convenient.