in a slider crank mechanism maximum displacement of piston is equal to 2r r 3r or 4r where r is

Step 1: Understand the slider crank mechanism. In this mechanism, a crank rotates, and this rota

In a slider crank mechanism maximum displacement of piston...

Transcript

00:01 High, so we are given that a one cylinder slider crank mechanism.

00:09 So in the first part we need to find the exact solution for position velocity.

00:15 First of all let us draw the free body diagram which will show up the required function that we need to perform in regards to the given crank system.

00:28 So let's suppose this is the angle theta, this is o point, this is a point and this is nothing but the angle beta.

00:37 This complete length is about l.

00:40 So this is what the point b.

00:42 Here is the point b1.

00:44 From there to this much of the point the distance will be x.

00:48 So x be the length of connecting rod.

00:50 Now obliging ratio, let's say p can be calculated as l by r.

00:58 Theta is the angle of crank.

00:59 Which can be given by the formula theta is equals to omega into t.

01:04 First of all if we suppose this as n.

01:07 So n should be equals to l by r will give me the length of rod l is equals to n times of r.

01:16 From the figure applying the trigonometry property l sine beta this is equals to r sine of theta.

01:24 This implies that cosine of beta is equals to under root over 1 minus sine of 2 theta by r square.

01:34 This should be equals to under root over r square minus of sine square of theta divided by r square.

01:42 So this is square here.

01:44 So first of all for displacement x we have to use from the figure as x is equals to c.

01:51 This can be given by bb1 which is equals to b1 0 to b0.

01:59 So that can be represented as c.

02:01 B to node the distance is r plus l minus of for b node it is l cosine of beta plus r cosine of theta.

02:13 So substituting all the values we get r 1 minus cosine of theta plus r n minus of under root over n square minus sine square of theta.

02:24 We get the displacement equation as x is equals to r in bracket 1 minus cosine of theta plus r minus of this should be r here under root over r square minus sine square of theta.

02:41 So this is what one of the answer to first part.

02:43 Now also we have to find the expression for velocity...

Question

in a slider crank mechanism maximum displacement of piston is equal to 2r, r, 3r or 4r where r is crank radius

Question

in a slider crank mechanism maximum displacement of piston is equal to 2r, r, 3r or 4r where r is crank radius

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