# Equal speeds condition when driving & driven shafts connected by Hooks joint - Theory of Machines - 1

Q.  Which relation is used to denote condition for equal speeds, when driving and driven shafts are connected by Hook's joint?
- Published on 06 Aug 15

a. tan θ = ± √cos α
b. tan θ = ± √cot α
c. tan θ = ± √sin α
d. cot θ = ± √cos α

ANSWER: tan θ = ± √cos α

#### Discussion

• Sravanthi   -Posted on 21 Oct 15
- Hooke's joint is used to connect two non-parallel and intersecting shafts.

- Hooke's joint is used in multiple drilling machines to transmit power to different spindles.

- For the condition of equal speeds, ω1 = ω2 . Substituting this value in the given below equation,

ω2 / ω1 = (cos α) / (1 – cos2 θ sin2 α)

we get,
tan ϑ = ± √cos α

Hence through this equation it is concluded that at four values of θ are obtained when ω1 = ω2

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