# Homework Help: Prove mathematically that the lengths of the crank...

1. Dec 2, 2016

### maths85

1. The problem statement, all variables and given/known data
Design an offset slider-crank mechanism which has the following specifications:
1. Stroke length of slider block C = 150 mm
2. Advance-to-return time ratio = 1.2
3. Offset height h = 50 mm

Prove mathematically that the lengths of the crank and of the connecting rod are AB
= 71 mm and BC = 178 mm respectively to the nearest millimetre.

I would appreciate any help to find the process and ecuations necessary to solve this problem.
I have tried to use differet ways to solve it but it gets very complicate and it suppose to be something easier..

I found a possible solution using the next representation and equations:

2. Relevant equations

We take into account that:

When I got this quadratic equations I realise that its getting too complicate, plus even solving this equations at the end there is not solution and I need to use a graphic way to find the length of the crank, and I have to use only mathematically process to solve it, I cant solve it graphically.

Another possible solution that I found was using the next steps:

3. The attempt at a solution
Another way that suppose to drive to calculate the lengths is using complex numbers but I started and it is quite complicate also.

Does anybody know where could I find a non very complicate way to solve this, my teacher told me that it suppose to be a mathematical method that is not very complicate?
I dont need anybody to make it for me, only a little help to where could I find formulas and the right approach to solve it.

Thank You.
Have a good day

2. Dec 2, 2016

### Nidum

Back solve from the given answers .

3. Dec 3, 2016

### maths85

Hello.
Iam still stuck, I am using the ratio formula to get the angles, I tried using the cosine and sin rules, but still not going anywhere, with these formulas that I put in the last part of my post I cant get anywhere because I dont have enough data, I need to use the length to go somewhere and that exactly what I need to calculate, so I cant use this data.
Any possible advice of how to proceed?
I guess I am missing something that I can´t realise