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Kinematics of Machines

UNIT-2CAMS

In machines, particularly in typical textile and automatic machines, many parts needto be imparted different types of motion in a particular direction.

This is accomplished by conversion of the available motion into the type of motionrequired. Change of circular motion to translatory (linear) motion of simple harmonictype and vice-versa and can be done by slider-crank mechanism as discussedpreviously.

But now the question arises, what to do when circular or rotary motion is to bechanged into linear motion of complex nature or into oscillatory motion.

This job is well accomplished by a machine part of a mechanical member, known ascam.

3.1 A cam may be defined as a rotating, reciprocating or oscillating machine part, designed toimpart reciprocating and oscillating motion to another mechanical part, called a follower.

o A cam and follower have, usually, a line contact between them and as such they

constitute a higher pair. o The contact between them is maintained by an external force which is generally,

provided by a spring or sometimes by thesufficient weight of the follower itself.

3.2 Classification of CamsCams are classified according to a) shape,b)Follower movement and c) Type ofconstraints of the follower

3.2.1 According to Shape

3.2.1.1 Wedge and Flat CamsIn Fig. 3.1 (a), on imparting horizontal translatorymotion to wedge, the follower translates vertically Fig. 3.1 (b) the wedge has curved surface at its top.The follower gets a oscillatory motion when ahorizontal translatory motion is given to the wedge.In Fig. 3.1(c), the wedge is stationary, the guide isimparted translator motion within the constraintprovided. This results in translatory motion of thefollowerIn Fig3.1(d), instead of a wedge, a rectangular blockor a flat plate with a groove is provided. Whenhorizontal translatory motion is imparted to theblock, the follower is constrained to have a vertical translatory motion.

Fig. 3.1 Classification of the CAMs according to their shape (wedge and flat cams)


3.2.1.2 Radial or Disc Cam

In radial or disc cams the shape of working surface (profile) is such that the followersreciprocate in a plane at right angles to the axis ofthe cam as shown in Fig. 3.2 (a). It is called asradial cam because the motion of the followersobtained is radial (Fig. 3.2). A differently shapedradial cam is also shown in Figs (b-e).

3.2.1.3 Cylindrical Cams

Cylindrical cams have been shown in Figs 3.3 (a andb). In Fig3.3 (a) the follower reciprocates whereas inFig. 3.2(b) the follower oscillates. Cylindrical camsare also known as barrel or drum cams.

3.2.1.4 Spiral CamsIt is shown in Fig, 3.4. The cam comprises of a plateon the face of which a groove of the form of a spiral iscut. The spiral groove is provided with teeth whichmesh with pin gear follower. This cam has a limiteduse because it has to reverse its direction to reset theposition of the follower. This cam has found its use incomputers.

Fig. 3.2 Classification of the CAMs according to their shape (Radial or disc cam)

Fig. 3.3 Classification of the CAMs according to their shape (cylindrical cams)

Fig. 3.4 Classification of the CAMs according to their shape (spiral cams)


3.2.1.5 Conjugate Cams

As the name implies, the cam comprises of two discs,keyed together and remain in constant touch with tworollers of a follower as shown in Fig. 3.5. This cam isused where the requirement is of high dynamic load, lowwear, low noise, high speed and better control offollower.

3.2.1.6 Globoidal CamsThis cam has two types of surfaces :convex and concave. A helical contour iscut on the circumference of the surface ofrotation of the cam as shown in Figs3.6(a) and (b). The end of the follower isconstrained to move along the contour andthen oscillatory motion is obtained. In thiscam, a large angle of oscillation of thefollower is obtained.

3.2.1.7 Spherical CamsIn this cam, as shown in Fig. 3.7, the cam isof the shape of a sphere on the peripheral ofwhich a helical groove is cut. The rollerprovided at the end of the follower rolls in thegroove causing oscillatory motion to thefollower in an axis perpendicular to the axisof rotation of the cam.

3.2.2 According to Follower Movement3.2.2.1 Rise-return-rise (RRR)In this type of cam, its profile or contour is such thatthe cam rises, returns without rest or dwell, andwithout any dwell or rest, it again rises. Followerdisplacement and cam angle diagram for this type ofcam is shown in Fig. 3.8.

Fig. 3.5 Classification of the CAMs according to their shape (Conjugate cams)

Fig. 3.6 Classification of the CAMs according to their shape (Globoidal cams)

Fig. 3.7 Classification of the CAMs according to their shape (Spherical cams)

Fig. 3.8 Classification of the CAMs according to follower movement (RRR)


3.2.2.2 Dwell, Rise-return Dwell (DRRD)

In this type of cam after dwell, there is rise of thefollower, then it returns to its original position anddwells for sometimes before again rising. Generally,this type of cam is commonly used. Its displacementcam angle diagram is shown in Fig. 3.9.

3.2.2.3 Dwell-rise-dwell-return

It is the most widely used type of cam. In this, dwell isfollowed by rise. Then the follower remains stationary inthe dwell provided and then returns to its originalposition[Fig.3.10].

As may be seen in the follower-displacement verses cam angle diagram, shown in Fig. 3.11in this cam, the fall is sudden which necessities enormous amount of force for this to takeplace.

3.2.3 According to Type of Constraint of theFollower

3.2.3.1 Pre-loaded Spring CamFor its proper working there should be contactbetween the cam and the follower throughout itsworking, and it is achieved by means of a pre-loaded spring as shown in Fig. 3.11(a) and (b),etc.

Fig. 3.9 Classification of the CAMs according to follower movement (DRRR)

Fig. 3.10 Classification of the CAMs according to follower movement (DRDRD)

Fig. 3.11 Classification of the CAMs according to follower movement (DRD)

Fig. 3.11 Classification of the CAMs according type of constraints (pre loaded or spring Cam)


3.2.3.2 Positive Drive CamIn this case, the contact between the cam and thefollower is maintained by providing a roller at theoperating end of the follower. This roller operates inthe groove provided in the cam. The follower cannotcome out of the groove, as shown in Fig. 3.12.

3.2.3.3 Gravity Drive CamIn this type of cam,the lift or rise of thefollower is achievedby the rising surfaceof the cam (Fig. 3.13) and the follower returns or falls due toforce of gravity of the follower. Such type of cams cannotbe relied upon due to their uncertain characteristics.

3.3 Classification of FollowersFollowers may be classified in three different ways :

a) Depending upon the type of motion, i.e. reciprocating or oscillating.b) Depending upon the axis of the motion, i.e. radial or offset.c) Depending upon the shape of their contacting end with the cam.

Those of followers falling under classification (a) and (b) have already been dealt with asindicated above. Followers of type (c) will be taken up now.

3.3.1 Depending upon the Shape of their Contacting End with the Cam

Under this classification followers may be divided into three types:

3.3.1.1 Knife-edge FollowerKnife-edge followers are generally, not used because of obvioushigh rate of wear at the knife edge. However, cam of any shape canbe worked with it. During working, considerable side thrust existbetween the follower and the guide.

Fig. 3.12 Classification of the CAMs according type of constraints (Positive Drive CAM)

Fig. 3.13 Classification of the CAMs according type of constraints (Gravity drive CAM)

Fig. 3.14 Knife-edge Follower


3.3.1.2 Roller Follower

In place of a knife edge, a roller is provided at the contacting end of thefollower, hence, the name roller follower. Instead of sliding motionbetween the contacting surface of the follower and the cam, rollingmotion takes place, with the result that rate of wear is greatly reduced.In roller followers also, as in knife edge follower, side thrust is exertedon the follower guide. Roller followers are extensively used instationary gas and oil engines. They are also used in aircraft engines dueto their limited wear at high cam velocity. While working on concavesurface of a cam the radius of the surface must be at least equal toradius of the roller.

3.3.1.3 Flat or Mushroom FollowerIn flat followers, high surface stresses are produced in the flatcontacting surface. To minimise these stresses, spherical shapeis given to the flat end, as shown in Fig. 3.16. The curved facedor spherical faced followers are used in automobile engines.With flat followers, it is obviously, essential that the workingsurface of the cam should be convex everywhere.

3.4 Terminology of Cam and Follower

3.4.1 The Cam Profile

Fig. 3.15 Roller Follower

Fig. 3.16 Flat or Mushroom follower

Fig. 3.17 CAM Profile


The working contour of a cam which comes into contact with the follower to operate it, isknown as the cam profile. In Fig. 3.17, A-B-C-D-A is the cam profile or the working contour.

3.4.2 The Base CircleThe smallest circle, drawn from the centre of rotation of a cam, which forms part of the cam profile, is known as the base circle and its radius is called the least radius of the cam. A circlewith centre O and of radius OA forms the base circle. Size of a cam depends upon the size of the base circle.

3.4.3 The Tracing PointThe point of the follower from which the profile of a cam is determined is called the tracing point. In case of a knife-edge follower, the knife edge itself is the tracing point. In roller follower, the centre of roller is the tracing point.

3.4.4 The Pitch CurveThe locus or path of the tracing point is known as the pitch curve. In knife-edge follower, thepitch curve itself will be the cam profile. In roller follower, the cam profile will bedetermined by subtracting the radius of the roller radially throughout the pitch curve.

3.4.5 The Prime CircleThe smallest circle drawn to the pitch curve from the centre of rotation of the cam is called asthe prime circle. In knife-edge follower, the base circle and the prime circle are the same. Inroller follower, the radius of the prime circle is the base circle radius plus the radius of theroller.

3.4.6 The Lift or StrokeIt is the maximum displacement of the follower from the base circle of the cam. It is also called as the throw of the cam. In Fig. 3.17, distance BB and CC is the lift, for the roller follower

3.4.7 The Angles of Ascent, Dwell, Descent and Action Refer Fig. 3.17, the angle covered by a cam for the follower to rise from its lowest

position to the highest position is called the angle of ascent denoted as 1. The angle covered by the cam during which the follower remains at rest at its highest

position is called the angle of dwell, denoted by 2 The angle covered by the cam, for the follower to fall from its highest position to the

lowest position is called the angle of descent denoted as 3. The total angle moved by the cam for the follower to return to its lowest position after the

period of ascent, dwell and descent is called the angle of action. It is the sum of 1, 2 and 3.

3.4.8 The Pressure AngleThe angle included between the normal to the pitch curve at any point and the line of motion of the follower at the point, is known as the pressure angle. This angle represents the steepness of the cam profile and as such it is very important in cam design.

3.4.9 The Pitch PointThe point on the pitch curve having the maximum pressure angle is known as the pitch point.


3.4.10 The Cam AngleIt is the angle of rotation of the cam for a certain displacement of the follower.

3.5 Type of follower motion Cam follower systems are designed to achieve a desired oscillatory motion. Appropriatedisplacement patterns are to be selected for this purpose, before designing the cam surface.The cam is assumed to rotate at a constant speed and the follower raises, dwells, returns to itsoriginal position and dwells again through specified angles of rotation of the cam, duringeach revolution of the cam

Some of the standard follower motions are as follows:They are, follower motion with,a) Uniform velocityb) Modified uniform velocityc) Uniform acceleration and decelerationd) Simple harmonic motione) Cycloidal motion

3.5.1 Displacement diagrams:In a cam follower system, the motion of the follower is very important. Its displacement canbe plotted against the angular displacement θ of the cam and it is called as the displacementdiagram. The displacement of the follower is plotted along the y – axis and angulardisplacement θ of the cam is plotted along x-axis. From the displacement diagram, velocityand acceleration of the followercan also be plotted for different angular displacements θ ofthe cam The displacement, velocity and acceleration diagrams are plotted for one cycle ofoperation i.e., one rotation of the cam. Displacement diagrams are basic requirements for theconstruction of cam profiles. Construction of displacement diagrams and calculation ofvelocities and accelerations of followers with different types of motions are discussed in thefollowing sections


a) Follower motion with Uniform velocity:Fig.3.18 shows the displacement, velocity and acceleration patterns of a follower havinguniform velocity type of motion. Since the follower moves with constant velocity, during riseand fall, the displacement varies linearly with θ. Also, since the velocity changes from zero toa finite value, within no time, theoretically, the acceleration becomes infinite at the beginningand end of rise and fall.

Fig. 3.18 Follower motion with Uniform velocity


b) Follower motion with modified uniform velocity:It is observed in the displacement diagrams of the follower with uniform velocity that theacceleration of the follower becomes infinite at the beginning and ending of rise and returnstrokes. In order to prevent this, the displacement diagrams are slightly modified. In themodified form, the velocity of the follower changes uniformly during the beginning and endof each stroke. Accordingly, the displacement of the follower varies parabolically duringthese periods. With this modification, the acceleration becomes constant during these periods,instead of being infinite as in the uniform velocity type of motion. The displacement, velocityand acceleration patterns are shown in Fig.3.19

3.19 Follower motion with modified uniform velocity


c) Follower motion with uniform acceleration and retardation (UARM):Here, the displacement of the follower varies parabolically with respect to angulardisplacement of cam. Accordingly, the velocity of the follower varies uniformly with respectto angular displacement of cam. The acceleration/retardation of the follower becomesconstant accordingly. The displacement, velocity and acceleration patterns are shown in Fig.3.11

Fig. 3.11 Follower motion with uniform acceleration and retardation (UARM):


d) Simple Harmonic Motion:In Fig.3.12, the motion executed by point Pwhich is the projection of point P on the verticaldiameter is called simple harmonic motion. Here,P moves with uniform angular velocity ωp, alonga circle of radius r (r = s/2)

Fig. 3.12 Simple Harmonic Motion


Fig. 3.13 Simple Harmonic Motion


e) Cycloidal motion:Cycloid is the path generated by a point on the circumference of a circle, as the circle rollswithout slipping, on a straight/flat surface. The motion executed by the follower here, issimilar to that of the projection of a point moving along a cyloidal curve on a vertical line asshown in Fig.3.15.

The construction of displacement diagram and the standard patterns of velocity andacceleration diagrams are shown in Fig. 3.16. Compared to all other follower motions,cycloidal motion results in smooth operation of the follower

The construction of displacement diagram and thestandard patterns of velocity and accelerationdiagrams are shown in Fig.3.16. Compared to allother follower motions, cycloidal motion results insmooth operation of the follower. The expressionsfor maximum values of velocity and acceleration ofthe follower are shown below.

Fig. 3.15 Cycloidal motion


Fig. 3.16 Cycloidal motion

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