三维激光切割头空间位姿变化的平顺性直接影响机床切割效率、安全和稳定性。建立了三维激光切割机五轴联动运动学模型，分析切割轨迹刀位点几何信息转换为机床五个运动轴空间坐标的可选值。结合B和C旋转轴运动部件间的摩擦力、质量和转动惯量，建立相邻刀位点间的旋转轴旋转运动耗能模型。将完整切割环上旋转轴运动最低总耗能作为优化目标，通过Dijkstra最小路径优化算法，获得完整切割环上的最佳切割方式。通过实例分析，该方法可避免B和C轴瞬间摆动过大情况，提高了切割头运动的平顺性。

The changes of three-dimensional (3D) laser cutting head′s orientation directly affect the cutting efficiency, security and stability of machine tool. A kinematic model of 3D laser cutting machine is established, and optional values are analyzed when geometric information of cutter location points on the cutting trajectory is transformed to space coordinates of five axes. Based on the friction between moving parts and the quality and the inertia of rotation axis, this paper establishes an energy model of the rotational motion of B, C-rotation axis between adjacent cutter location points. The optimization goal is the lowest total energy consumption of rotational motion of B, C-rotation axis on the complete cutting ring, then a minimum energy consumption path can be found by Dijkstra algorithm. Through example calculation, this method can avoid the momentary swing of B, C-rotation axis and enhance the movement smoothness of laser cutting head.