Abstract. This paper describes a computer-aided design for design of the concave globoidal cam with cylindrical rollers and indexing turret. Abstract—This paper describes a computer-aided design for design of the concave globoidal cam with cylindrical rollers and swinging follower. Four models. Globoidal Cams combine great strength and stiffness with compactness. MechDesigner will calculate the Globoidal cam profile to machine accuracy (no.

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Globoidal cam mechanisms are widely used in industry. Compared to other cam-follower systems, the globoidal cam-follower mechanisms have many advantages, such as: They are widely used in machine tools, automatic assembly lines, paper processing machines, packing machines, and many automated manufacturing devices. In term of the shape, globoidal cam is one of the most complicated cams.

The most important task when modelling the globoidal cams is to represent their working surfaces. The working surfaces of the globoidal cams are the surfaces that contact with the roller surfaces. These surfaces are very complex and it is very difficult to create them accurately. Up to now, a number of works dealing with finding the way to describe accurately these surfaces have been proposed. Some programs can draw and display the draft of the cam contour, or create the solid model.

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Some other researchers also described mathematicaly the cam surface, but they used computer to develop a package, which was a combination of AutoCAD R14, 3D Studio Max, and VBA, to generate the surfaces of the roller gear cam En-hui et globoidap. They represented the surface geometry of the cam as globoieal swept surfaces of the tool paths. In general, the works mentioned above have used the mathematical expressions for the globoidal cam surfaces and various cam laws as the input data to generate the cam surfaces.

These angular displacements can be extracted from the NC program generated by some special sofwares that are specialized for cam mechanisms. They can also be obtained from the follower displacement equations. In this study, the concave globoidal cam with swinging roller follower is modeled from angular input and output displacements. The objective of the chapter is to introduce some effective methods for modelling concave globoidal cam.

In this case study, the input data for modelling are the angular input and output displacements of the cam and the follower. Furthermore, besides modelling methods, some important techniques that are useful for designers to find out the most accurate model are also represented.

The outline of the chapter is as follows. Section 2 presents the theoretical background of concave globoidal cam.

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In section 3 we describe in detail some modelling methods that can be used to create the globoidal cam surfaces. An application example is presented in Section 4. Finally, conclusion remarks are given in Section 5. There are two types of globoidal cams. The first one is the globoidal cam that has a groove on its surface and the roller follower oscillates when the cam rotates. This type has two subtypes which are convex and concave Figure 1. These cams are used for small angles of follower oscillation.

The second one has one or more ribs on a globoidal body. This type is also called roller gear cam or Ferguson drive Rothbart, The two surfaces of the rib always contact with the rollers cylindrical, spherical or conical of the follower. This follower may oscillate about its axis or have an intermittent rotation. Figure 2 shows two subtypes of the concave globoidal cam: The rib of these cams looks like a thread or a blade so that sometimes they can be called thread-type or blade-type globoidal cams.

In this study, the single thread-type is the globoidal cam that we will deal with. Figure 3 illustrates the geometrical relationships between a concave globoidal cam with an oscillating follower. In Figure 3, the development plane is the plane that is normal to the axis of the roller and located anywhere along the length of the roller.

The intersection point between the development plane and the axis of the roller is the pitch point P. Datum plane is the plane normal to the cam axis and contains the follower axis.

The angular displacement of the roller is measured from this plane. If the start point is encountered after the datum plane then 0 is positive. It is the height of the point P and presented as.

## Globoidal cam indexer

Obviously, the coordinates of the pitch points on the rollers can be calculated if the angular input and output displacements globoidwl known. From these coordinates and some other information, the pitch surfaces of the cam can be modeled. There are some methods used to model concave globoidal cams. The most important task in the modelling procedure is to create the working surfaces of the cam.

Once these surfaces are created, other surfaces of the cam can be easily formed later. Here, we introduce two groups of methods that can be used to create the cam surfaces, namely Pitch surface-based methods and Standard cutter-based method. The two axes of two rollers in this case study will generate two pitch curved surfaces.

The working surfaces of the cam can be obtained from the pitch surfaces by globoidl them a distance that is equal to the radius of the roller. There are several methods to get the pitch surface. The followings are three methods that can be used to create the pitch surface. Sweep a straight line with two constraints Figure 4: The relationship between pairs andh andR and can be globoidxl in graphs.

This method is similar to the previous method but here the two pitch surfaces are created at the same time. Two of them are collinear with the axes of the two rollers. The last one connects them together. Sweep a straight line that is collinear with the roller axis. The two end points of this line must lie on two curves Figure 6. One of these curves is a circle in the datum plane.

This circle goes through the intersection point of the roller axes and its center is in the cam axis and it is also called the origin trajectory. The other curve is a three-dimensional 3D curve. This 3D curve is the locus of a point, which located on the roller axis it can be the pitch pointwhen the follower rotating. The coordinates of that point satisfy formulas 3 and 4 above. An end mill cutter can generate the surfaces of a globoidal globoidxl. If the diameters of the cutter and the roller are equal, the motion of the cutter will be similar to that of the roller in the machining process, and of course, the cutter must rotate about its axis roller axis.

The sweep surface of the tool path can represent the working surface of the cam. The following is one way that can be used to get the cam surface. Cut a bank by sweeping a rectangular section Figure 7 to form the cxm surfaces if the following constrains are performed:.

The width of the section is equal to the diameter of the roller. The length of the section satisfies the following formula.

Two points on the section, which are intersection points between the symmetry axis of the section and its edges, must follow two 3D curves. These curves are loci of two points, which are on the roller axis, when the follower rotates.

One of these curves is the origin trajectory. The curves which are used in the curves- based method can be applied here. In theory, geometric errors may exist on every model.

These errors may be so very high that the model cannot be acceptable. Hence, after modelling, models must be checked to find out the best one among them. The implementation of those methods is presented in a form of an illustrated example in the next section.

Besides, some other important tasks to check the model are included as well. Given a concave globoidal cam with an oscillating follower that has two cylindrical rollers. The angle between two axes of the rollers is 60 0. The increment of the input angle of the cam is 0.

The angular input and output displacements are given in a table that consists of pairs of corresponding angles. Some of them are presented in Table I in the appendix. To observe easily, the relationship between the angular input and vam displacements is showed in Figure 8.

The following are some other parameters of the system, which are showed in Figure 2: The accuracy of the system is set to 0. Create a revolution surface of the globoidal body of the cam Figure 9 a.

Create 3 graphs for the angle between the sweeping line and the datum plane Figure 9 bthe height of the pitch tloboidal on the sweeping line, and the distance radius from the pitch point to the cam axis. These graphs show the dependence of the three above parameters on the angular output displacement of the cam. Create the upper pitch surface by using the Variable Fam Sweep command Figure 9 c. The origin trajectory in this case is the circle which is the intersection between datum plane and the cam body.

Constrains for this command are formulas that have the form as. Create the two pitch surfaces at the same time by using the Variable Section Sweep command Figure 1 0a ca, the same constrains in step 3 in the first method. Create a revolution surface of the globoidal body of the cam Figure 1 1a. Create the origin trajectory and two 3D curves Figure 1 1b. Create the two pitch surfaces by using the Variable Section Sweep command Figure 1 1c.

Create a revolution blank of the cam body Figure 1 2a. Create the origin trajectory and two 3D curves Figure 1 2b.