The design of any machinery and appliances is made by the separate details connected among themselves. Their form is defined by a combination of the planes and various curve surfaces which are often crossed and form lines of mutual crossing.
Instruction
1. Tasks of finding of lines of crossing allow to solve the wide range of questions on designing of technical details. The basis of the majority of decisions includes creation of the line by means of the auxiliary planes. As cylinders are the surfaces of rotation with the crossed rotation axes, as secants of the planes spheres, as a rule, are used. Before building the line of crossing, draw two cylinders with the crossed rotation axes. The center of an axis of rotation of cylinders is the center of secants of spheres.
2. Define extreme general points of intersection – the biggest and smallest radius. The maximum radius of a secant of the sphere equals to distance from the center of an axis of rotation to the farthest point of intersection of two surfaces. Carry out a sphere circle with the maximum radius and find a point of its crossing with cylinders – a point 1.
3. The minimum radius of a secant of the sphere decides on the help of two normals of K1 and K2. As the sphere with the smallest diameter does not cross two cylinders at once, as the minimum radius of the sphere the maximum normal is accepted. Carry out a sphere circle with the minimum radius and find a point of its crossing with cylinders – a point 2.
4. Define the lowest point of intersection of cylinders. For what construct a secant the sphere which crosses the first cylinder on G circle, and the second cylinder – on a circle of D. The frontal projection of a circle of G coincides with a projection of an axis of rotation of the second cylinder. The point of intersection of two circles – G and D – is also the lowest point 3.
5. Construct intermediate points of intersection of two cylinders, using a method of creation of any spheres to similarly previous action. As a result you receive two points of the line of crossing – 4 and 5. Connect points 1-5 smooth lines, thereby forming the required line of crossing for two cylinders.