基于球面曲线的空间非匀速行星轮系分插机构逆向设计

Reverse design of transplanting mechanism with spatial planetary gear train based on spherical curve

针对目前非圆锥齿轮行星系分插机构运动轨迹、姿态设计中存在的对机构参数选择和参数对设计目标影响的不确定性问题,提出一种基于球面曲线的空间行星轮系机构逆向设计方法。在利用样条曲线描述光滑、连续、封闭理想平面插秧轨迹的基础上,采用保测地曲率投影方式将平面轨迹映射到给定球面获得目标球面轨迹;由二杆三自由度空间开式机构复演球面轨迹,并根据杆件的空间几何关系建立行星轮系机构的总传动比反求模型;通过在杆件上依附非圆锥齿轮、非圆齿轮,实现基于给定运动要求的各级传动比分配和齿轮节曲线再现;利用Matlab编写反求程序,并在高速水稻宽窄行分插机构的设计中,实现非圆齿轮—非圆锥齿轮行星轮系宽窄行分插机构的参数反求。最后,通过设计并加工机构实物进行台架试验,由高速摄像技术测试并得到了与给定球面轨迹一致的插秧轨迹,验证了方法的可行性,为宽窄行分插机构设计提供了新的方法。

The transplanting mechanism is an end manipulator which picks seedlings from a seedling box and pushes them into a rice field. A wide-narrow distance mechanism is a kernel part of the rice transplanter to place seedlings in a wide row and narrow row alternation. Because of the spatial movement property of a bevel gear pair, and the requirement of variable speed transmission, a noncircular bevel gear was widely used in a wide-narrow transplanting mechanism design. On the condition of a determinate transmission scheme, how to obtain a sound planting trajectory and proper picking posture which is important for the wide-narrow distance transplanting mechanism to achieve upstanding and fewer damaged seedlings in planting work becomes a key issue. In general, putting forward a new mechanism, building a calculate model, and compiling a parameters optimization program are the three main steps for transplanting mechanism design. But there is some uncertainty of parameters-choosing and parameters effecting design goals in the design of the trajectory and planting paw posture in the traditional way. Furthermore, the special noncircular gear such as elliptical （or bevel） gears, eccentric-noncircular （or bevel） gears whose pitch curve are accessible to expression are often used in the transmission scheme design, which limits the formation of trajectory shape and planting paw posture. A new way to design a spatial planetary noncircular gear train by using reverse design methods was put forward based on the spherical curve. An ideal plane curve which is smooth, continuous, and closed was expressed by a free spline curve, and then a spherical curve was obtained by mapping the ideal plane curve onto the spherical surface with a preserved geodesic curvature. A two bar mechanism with three degrees of freedom was used to describe the spherical curve. According to the spatial geometric relationship between the two bars and the center of sphere, the transmission ratio model was established. The transmission ratio of every single gear pair and the pitch curve of every gear were resolved by attaching a noncircular gear and a noncircular bevel gear to the two bar mechanism with three degrees of freedom. The parameter inverse and design program for a wide-narrow distance transplanting mechanism with noncircular gears and noncircular bevel gears, based on the development platform of MATLAB, was compiled and the ideal spherical surface trajectory was obtained by modifying the data point of plane trajectory. In addition, a group of mechanism parameters was reversed by the method of human-computer conversation afterward. Finally, a model machining of the transplanting mechanism was processed and a testing trajectory, similar to the theoretical trajectory was gained, which verified the feasibility of this reverse design method and supplied a new method for the design of a wide-narrow distance transplanting mechanism.