Theory Of Machine - Study Mode

[#166] In a gear having involute teeth, the normal to the involute is a tangent to the
Correct Answer

(B) Base circle

Explanation

Solution: An involute gear tooth profile is the most commonly used tooth shape in gear design. It is generated by tracing the end of a taut string unwinding from a circle. The resulting curve is known as the involute of a circle . The base circle is the circle from which the involute profile is generated. It plays a crucial role in defining the geometry of involute gear teeth. Correct Answer: Option B – Base circle Explanation: In gears with involute teeth, the normal to the involute profile at any point is always tangent to the base circle from which the involute is generated. This is a fundamental property of the involute curve. As the involute curve is traced by unwinding a string from the base circle, the direction of the tension (which is always tangential to the base circle) becomes the normal to the involute curve at the point of contact. This ensures constant velocity ratio and smooth power transmission in gear systems. Therefore, the line normal to the tooth profile at the point of contact always touches the base circle tangentially, confirming that the base circle is essential in defining the involute geometry. Why other options are incorrect: Option A: Pitch circle – The pitch circle is an imaginary circle where the gear teeth theoretically engage. It is not the reference circle for generating the involute profile. Option C: Addendum circle – This is the outermost circle of the gear, representing the tips of the teeth. It is not involved in generating the involute. Option D: Dedendum circle – This is the root circle of the gear, below the pitch circle. It also has no role in defining the involute shape. Conclusion: In a gear with involute teeth, the normal to the involute curve is always tangent to the base circle . Hence, the correct answer is Option B .

[#167] A mechanism is an assemblage of
Correct Answer

(C) Four or more than four links

Explanation

Solution: Definition: A mechanism is a combination of rigid bodies, known as links , connected by joints in such a way that they produce a desired motion when one of the links is given an input motion. The purpose of a mechanism is to convert input motion into a specific output motion. Correct Answer: Option C – Four or more than four links Explanation: In the theory of machines, a mechanism must be able to produce definite relative motion between its parts. For this to be possible, at least one link must be fixed , and the remaining links must be capable of moving in a controlled manner. According to Gruebler’s criterion for planar mechanisms, a mechanism generally requires a minimum of four links . When four or more links are connected in such a way that one is fixed and others can move, they form a kinematic chain , and if that chain is closed and at least one link is fixed, it becomes a mechanism. Therefore, a mechanism is typically defined as an assemblage of four or more links that transforms input motion into a controlled output motion. Why other options are incorrect: Option A: Two links – Two links connected by a joint form a single pair, not a mechanism. It cannot produce a constrained output motion by itself. Option B: Three links – Three links connected together form an incomplete kinematic chain and are generally not capable of producing definite motion without adding a fourth link. Option D: All of these – This is incorrect because only Option C meets the proper condition for forming a mechanism. Conclusion: A mechanism requires at least four links to produce constrained and useful motion. Hence, the correct answer is Option C .

[#168] In a four-bar chain it is required to give an oscillatory motion to the follower for a continuous rotation of the crank. For the lengths of 50 mm of crank and 70 mm of the follower, determine theoretical maximum length of coupler. The distance between fixed pivots of crank and followers is
Correct Answer

(B) Slightly less than 95 mm

[#169] The number of centers in a crank driven slider crank mechanism is
Correct Answer

(B) 2

[#170] The contact ratio is given by
Correct Answer

(C) $$frac{{{ ext{Length of the arc of contact}}}}{{{ ext{Circular pitch}}}}$$