Kinematics Final Print

8/13/2019 Kinematics Final Print

1/7

ENGINEERING DYNAMICS KINEMATICSMEC 2300


2/7

[ENGINEERING DYNAMICSKINEMATICS MEC 2300] 1

Kinematics Assignment

Introduction

Mechanisms are of utmost importance in mechanical engineering. A mechanism is used

to produce a mechanical transformation in a machine. The transformation may be but

not only:

In this particular case we are dealing with the last of the aforementioned

transformations that is the conversion of angular motion into rectilinear motion. Thereare several means by which one can achieve this, one of which may be the linkage

method. This method uses pins and linkage bars attached to one another with pins

sliding inside the differently shaped links. One such example is the Whitworth quick-

return mechanism.

Converting one speed to anotherspeed.

Converting one torque to anothertorque.

Converting rectilinear motion intoangular motion.

Converting angular motion intorectilinear motion.

A problem however arises with this approach in

many applications as these linkage mechanisms

b hi hl l h d diff t


3/7


Design

The aim of the assignment was to modify and re-design the model given to us so that

it is able to work continuously as a cam and follower mechanism. Initially one can

notice that the set-up, be it the slotted arm path or the offset distance of the rotating

axis to the vertical bar doesnt produce continuous linear motion.

Originally different concepts were put forward. One of the issues in the

design was the path prescribed by the pin. The choice of the latter is determined by

the type of cycle one requires. For example in relation to the automotive industry the

follower motion has to be expressed in relation to the angular displacement of thecam. This is because; as it is in most other applications the motion must be

synchronized.

To determine the right cam design for a specific use in a machine one must

have afollower displacement diagram. This will have the vertical displacement in this

case of the follower bar plotted against time (Graph 1) or angular cam displacement

(Graph 3) according to the constraints requested by the designer. This means that

this graph would show the relative positions of the vertical bar and the cam. It is

important to note that this whole mechanism would be part of a bigger system;

going back to the original reference, the automobile, the vertical displacement must

open and close a valve and the timing of this has to be close to perfection. Hence

these graphs alongside a good kinematic analysis will help choose the right design

for the path.

It is important to note that there are


4/7


= 1 + 2 + 3 + 4 + 5

These are the parameters involved:

Type of displacement Time (Sec) m

Starting Position 0 0

Rise 0.7 0.985Fall 0.3 1.623

Rise 1.3 1.606

Fall 0.55 1.101

Rise 0.3 0.133

H = Total follower displacement during the rise or fall. T = Total time period for the rise or fall. = Time into rise or fall interval that defines the instantaneous follower properties. = Rotation angle of cam during the rise or fall = Speed of the cam.

R = Magnitude of the instantaneous follower displacement at time t or cam angle . = Magnitude of the instantaneous follower velocity = dR/dt.

Before analyzing the system one

must establish the requirements of

this cam and follower mechanism.

The table on the right shows thetype of displacement required by

the follower at a given time in one

cycle. Using the equations below

the table one can find the cycle time

and consequently the angular

velocity of the cam is found. We are

assuming constant angular velocity

i hi

Table 1


5/7


Using simulation software the following of information was acquired. It is important to note that this

information takes into consideration the previously mentioned dynamic considerations such as

gravity forces and the smoothness of the curved path in relation to friction. Hence as illustrated ingraph 3, which plots the follower displacement versus angular displacement from table 2 and table 3,

in reality it is not a linear relationship but much different. This is also due to the fact that one can

never achieve absolute constant velocity or acceleration. For example when starting the mechanism a

starting torque is applied and this is varied accordingly until a steady angular speed is reached.

Once we obtain a follower

displacement diagram, we have a

relationship between the followerdisplacement and angular

displacement at various sections

in the cycle.

Using differentiation techniques

since the angular velocity is

assumed to be constantthroughout the follower motion

hence using a kinematic analysis

we can compute a Velocity vs

Angular Displacement (Graph 2)

and Velocity vs Time ( Graph 4).

From the last graph we can tell

what type of motion the system

d di d i l

R Velocity ofFollower

Rotation of cam

Seconds m m/s Degrees

0 0 0 0

0.15 0.146 1.138 17.18873

0.3 0.344 1.513 34.37747

0.45 0.602 1.921 51.5662

0.6 0.897 1.782 68.75494

0.75 0.866 -4.133 85.94367

0.9 -0.331 -7.683 103.1324

1.05 -0.633 0.323 120.3211

1.2 -0.551 0.672 137.5099

1.35 -0.44 0.792 154.6986

1.5 -0.312 0.92 171.8873

1.65 -0.162 1.098 189.0761

1.8 0.021 1.359 206.2648


6/7


Graph 3

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300 350 400

RectilinearDisplacementoffollower

Angular Displacement of cam in degrees

Rectilinear Motion of follower vs Angular Displacement of cam

Including Dynamic considerations"

Not including Dynamic considerations


7/7


-10

-8

-6

-4

-2

0

2

4

0 0.5 1 1.5 2 2.5 3 3.5

Follower velocity vs Time

Graph 4

The velocity on start-up is almost at constant acceleration. Before the peak it changes into cycloidal motion. The fall is a very abrupt one at very

sharp deceleration and followed by an almost immediate acceleration. Once again the acceleration reaches its peak with a cycloidal type of

motion. The second fall is similar to the first one. However the final rise has a decreasing acceleration.

Kinematics Final Print

Documents

Transcript of Kinematics Final Print