Question

Following in each of the following three mechanisms, the crank is the input link, 1) draw vectors with labeled angles 2) write the lop closure equation/vector equation in exponential form. 3) solve the unknown variables

Answer 1

Step-by-step explanation:

1.
`\theta_(4)=90^(\circ), \theta_(1)=\theta^(\circ)` (diagram)

2.

vector loop equation is

`\overline{R_(1)}+\overline{R_(2)}+\overline{R_(3)}=\overline{R_(4)}\\`

the exponential form,

`r_(1) e^(j \exp (0))+r_(2) e^{j \theta_(2)}+r_(3) e^{j \theta_(3)}=r_(4) e^(j(90))`

`e=\cos \theta+j \sin \theta`

3.

Real part,
`r_(1)+\ r_(2) \cos \theta_(2)+\ r_(3) \cos \theta_(3)=0` (i)

Imaginary part,
`0+r_(2) \sin \theta_(2)+r_(3) \sin \theta_(3)=r_(4)` (ii)

From above equation,we get unknown variables,

Now,
`\theta_(2), \theta_(3) \& r_(4)`

If
`\theta_(2)` is given,

From (i),
`\theta_(3)=\cos ^(-1)\left((-r_(1)-r_(2) \cos \theta_(2))/(r_(3))\right)`

and from (ii), we get

`x_(4)=r_(2) \sin \theta_(2)+r_(3) \sin \left[\cos ^(-1)\left((-\gamma_(1)-r_(2) \cos \theta_(2))/(r_(3))\right)\right]`