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The displacement of the reciprocating roller follower, when it has contact with the straight flanks of the tangent cam, is given by (where r<sub>1</sub> = Minimum radius of the cam, r<sub>2</sub> = Radius of the roller follower and $$\theta $$ = Angle turned by the cam from the beginning of the follower displacement)

Correct Answer: $$\left( {{{\text{r}}_1} + {{\text{r}}_2}} \right)\left( {\frac{{1 - \cos \theta }}{{\cos \theta }}} \right)$$

Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$

The value of $$\frac{{\sec \theta \left( {1 - \sin \theta } \right)\left( {\sin \theta + \cos \theta } \right)\left( {\sec \theta + \tan \theta } \right)}}{{\sin \theta \left( {1 + \tan \theta } \right) + \cos \theta \left( {1 + \cot \theta } \right)}}$$        is equal to:

From the given data, calculate the acceleration of follower in m/s2 at the beginning of the lift for a symmetrical tangent cam operating a roller follower. Least radius of the cam is 30 mm; Roller radius is 17.5 mm. The angle of ascent is 75° and the total lift is 17.5 mm. The speed of the cam shaft is 600 r.p.m.

The velocity of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by (where $$\omega $$ = Angular velocity of the cam shaft)

$$\frac{{{{\left( {1 + \sec \theta \,{\text{cosec}}\,\theta } \right)}^2}{{\left( {\sec \theta - \tan \theta } \right)}^2}\left( {1 + \sin \theta } \right)}}{{{{\left( {\sin \theta + \sec \theta } \right)}^2} + {{\left( {\cos \theta + {\text{cosec}}\,\theta } \right)}^2}}},$$        0°

The expression $$\frac{{{{\left( {1 - \sin \theta + \cos \theta } \right)}^2}\left( {1 - \cos \theta } \right){{\sec }^3}\theta \,{\text{cose}}{{\text{c}}^2}\theta }}{{\left( {\sec \theta - \tan \theta } \right)\left( {\tan \theta + \cot \theta } \right)}},$$        0°

If $$\frac{{\sec \theta - \tan \theta }}{{\sec \theta + \tan \theta }} = \frac{1}{7},\,\theta ,$$     lies in first quadrant, then the value of $$\frac{{{\text{cosec}}\,\theta + {{\cot }^2}\theta }}{{{\text{cosec}}\,\theta - {{\cot }^2}\theta }}$$   is:

The linear velocity of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by

The acceleration of the reciprocating roller follower when it has contact with the straight flanks of the tangent cam, is given by

What is the value of [(cos 3θ + 2cos 5θ + cos 7θ)÷(cos θ + 2cos 3θ + cos 5θ)] + sin 2θ tan 3θ?