基于对偶四元数法的空间四连杆引纬机构运动学分析

Kinematics analysis of spatial four-bar linkage weft insertion mechanism based on dual quaternion

为全面分析机构参数对运动学特性的影响,首先利用对偶四元数法建立空间四连杆的运动学模型,根据运动学结果推导空间连杆输出摆角幅度和机构夹角θ之间的关系,并用几何法对其进行验证;根据运动学模型只含2个机构参数的特点,结合工艺要求,用Matlab绘制三维图,研究机构参数对引纬机构整体运动输出的影响。结果表明:空间连杆输出摆角幅度是机构夹角θ的2倍;夹角θ和引纬机构的剑头行程为线性关系;改变机构夹角θ和β使整体加速度减小的同时会使交接纬纱处加速度增大,且β=80°时的加速度变化比β=100°时大了近28.57%。

In order to comprehensively analyze the influence of mechanism parameters on kinematics,a kinematic model of spatial four-bar linkage weft insertion mechanism was established by dual quaternion. The relationship between the range of spatial four-bar linkage′s output angle and the mechanism included angle θ was derived according to the kinematic result,and the correctness of the conclusion was verified by the geometric method. Based on the fact that the mechanism has only two parameters of θ and β,combined with the technical requirements,the effect of mechanism parameters on the overall motion of weft insertion was studied with Matlab to draw three-dimensional charts. The result indicates that the range of spatial four-bar lintage's output angle is twice the mechanism with angle θ;the relationship between θ and the stroke of rapier head of weft insertion mechanism is linear;changing the values of θ and β will reduce the overall acceleration and increase the acceleration at the weft yarn transferring at the same time,and the acceleration variation at β= 80° is nearly 28.57%,larger than that of β= 100°.