envelope of a family of curves; two-parametric systems of curves; collector mechanism; Maple
A two-parametric system of close planar curves is defined in the introduction of the presented article. Next a theorem stating the existence of the envelope is presented and proved. A mathematical model of the collecting mechanism of the Horal forage trailer is developed and used for practical demonstrations. The collecting mechanism is a double joint system composed of three rods. An equation describing the trajectory of a random point of the working rod is derived using Maple. The trajectories of two close points of the working rod create a planar system of close curves, of which the envelope can be computed. As this computation is extremely complex, Maple was used to optimize the computations. Through this optimization the computation needed less memory and the processing time was shorter. In the final part the working areas and the corresponding envelopes of all rods defining the collecting mechanism are plotted.