Pimpri Chinchwad Polytechnic, Nigdi. Chapter 03-Cam And Followers PRESENTED BY Ms. M.R. Zade

Course Name: Theory of Machines C406 Year of Study: 2016-17 Identify machine elements, mechanisms and understand their kinematics and dynamics. C406.2 Draw velocity and acceleration diagram for different mechanisms. C406.3 Draw cam profile for different follower motions. C406.4 Select suitable drives and Mechanisms for a particular application. C406.5 Understand functions, operation and applications of flywheel, governor, brake, dynamometer, clutch and bearing. C406.6 Calculate unbalanced forces and balance the rotating masses.

Cams and follower mechanisms: Means for transforming rotary motion into reciprocating motion. Cams can be classified based upon the direction of motion of the follower relative to the axis of rotation of the cam. Plate Cams: Follower moves at right angle to axis of rotation of the cam. Cylindrical Cams: Follower moves in a direction parallel to cam axis.

Several different types of follower mechanisms exist Several different types of follower mechanisms exist. Radial follower: Centerline of follower intersects axis of rotation. Offset follower: Centerline of follower does not intersect axis of rotation. Swinging follower: Locating hinge point outside of cam’s surface enables point of contact existing between cam and follower to describe a circular arc.

Sensitivity of Followers: Not all followers have the same sensitivity to changes in cam contour. Different followers respond to cam profiles in different manners creating different paths.

Cams can be found in a variety of applications

Design procedure for use with cam and follower mechanisms 1) Identify motion requirements for follower using displacement diagram. Displacement diagram displays follower displacement as a function of cam rotation or time. 2) Establish radius of base circle of cam. Radius of base circle is equal to the distance from the lowest point on the cam periphery to the center of rotation of the cam. a) diameter of base circle must be at least as large as the diameter of the hub. b) In cams made integral with shaft, the diameter of the base circle must be at least equal to shaft diameter. c) Forces associated with follower motion will generate stresses in the cam shaft which must be sized to operate safely with the stress loading.

3) Modify radius of base circle using rise from displacement desired from followers as cam shafts rotates. Method used to modify base circle depends on type of follower. Interval from 00 -> 2100 has been divided into 14 subintervals producing an angle increment of ∆Ѳ = 210/14 = 150 for each subinterval. Base circle has been divided into corresponding angular increments of 150 with radial lines emanating from center of base circle every 150 . Length of any radial line emanating from center of base circle to periphery of cam can be determined as follows. where Length of radial line emanating from center of For subinterval #10 base circle to periphery of cam. radius of base circle rise of cam Lift of cam

Pressure angle: Angle between the normal to the cam at a point and the radial line passing through the point. Pressure angle can vary as you move from point to point along the periphery of the cam. Note: To prevent the possibility of binding a pointer follower the pressure angle is usually not permitted to exceed 300 . Q: At what point is Φ =0 for the previous example? Given displacement diagram below, assume cam shaft us rotating at 600 rpm and the left L=1in, plot velocity of follower as a function of time. Curves resulting in uniform velocities over various subintervals may generate large jumps in the values of acceleration for the follower.

Shape of displacement curve can be utilized to control velocity and/or acceleration of follower. Shape of displacement curve can be categorized based upon acceleration characteristics of follower. 1) Harmonic curve (Generates acceleration curve having a cosine dependencies) 2) Cycloidal curve (Generates acceleration curve having sine dependencies) 3) Constant acceleration (also termed parabolic) Graphical procedures may be utilized to generate displacement diagram for each category of curve. Geometry associated with a circle can be utilized to generate harmonic motion. 2 half circles are used to generate harmonic motion. One half circle dedicated to rise of follower, one half circle dedicated to fall of follower. Diameter of half circles equal lift L. Half circles are divided into angular increments which correspond to subinterval generated on horizontal axis of displacement diagram. Geometry associated with angular increments when projected onto displacement diagram generate harmonic motion. where X= rise of cam Ѳ= angle of cam Ѳ0 = angle of cam at L

Velocity and acceleration accompanying the displacement curve for harmonic motion can be obtained by utilizing the relationship Ѳ=ωt and differentiating. Equating describing velocity and/or acceleration for each category of curves as a function of position are provided in the table below.

Different types of motion can be combined into a displacement curve to achieve motion characteristics consisted with requirements of application. Example shown below depicts a displacement diagram possessing intervals exhibiting harmonic motion, dwelling characteristics and constant velocity motion.

Geometry of a circle can also be utilized to generate cycloidal curves Geometry of a circle can also be utilized to generate cycloidal curves. The geometry must be different from the configuration used in harmonic motion since the cycloidal curve is different from the harmonic curve.

2 options are available. Simplest technique utilizes rolling circle designated as A. Circumference of circle A is set equal to Lift L of cam Circumference of circle = 2Πr=L ->Πd=L where r= radius of circle D= Diameter of circle Circle is rolled up vertical axis without slippage. Point P on rolling circle is transferred to displacement diagram to generate cycloidal curve. Vertical axis is divided into subintervals corresponding to subintervals existing on horizontal axis of displacement diagram to enable proper correspondence to exist for transferring point P to displacement diagram.

When modifying base circle to generate can profile for use with roller, displacement diagram must be interpreted as rise associated with center of roller. Periphery of cam is determined from contact points establish by outside surface of roller. To develop cam profile, radius of base circle can be modified by an amount equal to radius of roller to generate a construction circle to serve as reference surface for generating cam profile from rise defined by displacement diagram. rc =rb +rr where rc – radius of construction circle rb- radius of base circle rr-radius of roller In example shown below, rc =rb +2rr

When generating a cam profile for use with a flat follower, the procedure is similar to the technique developed for constructing cams for use with roller followers. The base circle is modified and the rise from the displacement diagram is used to establish the separation distance between the flat face of the follower and the center of the base circle at various angles corresponding to intervals existing on horizontal axis of displacement diagram. Cam profile is established by drawing periphery of cam tangent to the face of the follower at the various angles.