Generalized kinematics of five-axis serial machines with non-singular tool path generation
Generalized kinematics of five-axis serial machines with non-singular tool path generation
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DOI：
10.1016/j.ijmachtools.2013.09.002
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发表时间：
2013-12
影响因子：
14
通讯作者：
Jixiang Yang;Y. Altintas
中科院分区：
文献类型：
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作者：
Jixiang Yang;Y. Altintas
典型的五轴机床有三个平移驱动器和两个旋转驱动器。本文提出了一个广义的运动学模型，该模型可以应用螺杆理论实现所有五轴机床的自动配置。首先，将每个运动单元建模为旋转关节、移动关节、工件或刀具。采用基础坐标系，通过螺旋理论对各运动单元进行数学组合。对旋转和平移运动的一般逆运动学解进行了评估。通过对样条刀具方向矢量进行变形，避免了五轴轮廓的奇异性。刀具的方向矢量用四元数空间中的五次b样条曲线表示，刀尖的运动用笛卡尔空间中的五次b样条曲线表示。这两条样条曲线构成了连续的刀具轨迹，并与刀尖位置的曲线长度参数进行拟合。如果刀具轨迹穿过机床的奇异区域，则在尊重加工公差的前提下，通过修改刀具方向样条在四元数空间中的控制点来实现刀具轨迹的变形。在自主开发的数控系统控制的五轴机床上，对所提出的运动学模块、刀具轨迹生成算法和避免运动奇异性的方法进行了实验验证。
Typical five-axis machine tools have three translational and two rotary drives. This paper presents a generalized kinematics model that allows automatic configurations of all five-axis machine tools using screw theory. First, each kinematic element is modelled as a revolute joint, prismatic joint, workpiece or cutting tool. The kinematic elements are mathematically assembled through screw theory by using the base coordinate system. The general inverse kinematics solutions for both rotary and translational motions are evaluated. The singularities in five axis contouring are avoided by deforming splined tool orientation vectors. The tool orientation vectors are represented by a fifth degree B-spline curve in a quaternion space, while the movement of tool tip is represented by a fifth degree B-spline curve in the Cartesian space. Both splines, which form theC3continuous tool path, are fitted to curve length parameter of the tool tip positions. If the tool path traverses the singular area of the machine, it is deformed by modifying the control points of the tool orientation spline in the quaternion space while respecting the machining tolerance. The proposed kinematics module, tool path generation algorithm and method for avoiding kinematic singularities are experimentally verified on a five-axis machine tool controlled by an in-house developed CNC system.