JNTU B.Tech III DYNAMICS OF MACHINERY Previous Question Paper (October - 2020 - R16)

To determine the input torque T on the link OA for static equilibrium, we apply the principle of virtual work or the method of static force analysis. Given the configuration, let θ be the angle of the crank OA with the line of stroke and φ be the angle of the connecting rod AB with the line of stroke. The position of the slider B is given by x = OA cos θ + AB cos φ.

Using the geometry of the mechanism, we have the relation OA sin θ = AB sin φ. For static equilibrium, the virtual work done by the input torque T and the external force F must sum to zero: T δθ + F δx = 0. Thus, T = -F (dx / dθ).

Differentiating the position equation with respect to θ:

From the geometric relation, differentiating gives OA cos θ = AB cos φ (dφ / dθ), so (dφ / dθ) = (OA cos θ) / (AB cos φ). Substituting this into the derivative of x:

The torque is then calculated as:

Given F = 2000 N, OA = 0.1 m, and AB = 0.45 m, the specific value of T depends on the angle θ. For a general configuration, determine φ using sin φ = (OA / AB) sin θ = (0.1 / 0.45) sin θ = 0.222 sin θ. Substitute θ and the resulting φ into the formula above to obtain the torque in N-m.

A gyroscopic couple is the torque exerted by a rotating body when its axis of rotation is forced to turn about an axis perpendicular to the original axis of rotation. When a disc of moment of inertia I rotates at an angular velocity ω (rad/s) and is subjected to an angular velocity of precession ωₚ (rad/s) about an axis perpendicular to the spin axis, a gyroscopic couple C is generated, defined as:

The stability of a motorcycle during a turn depends on the gyroscopic effect of the rotating wheels and the centrifugal effect. When a motorcycle takes a turn, the gyroscopic couple acts to either stabilize or destabilize the vehicle depending on the direction of the turn and the direction of wheel rotation.

The total effect is analyzed as follows:

• Gyroscopic Effect: If the wheels rotate in the same direction as the engine, the gyroscopic couple acts to tilt the motorcycle. When turning right, the couple acts to lift the front wheel or tilt the vehicle outward; when turning left, it acts to tilt the vehicle inward.
• Centrifugal Effect: The centrifugal force acts outward at the center of gravity, creating a destabilizing moment that tends to overturn the motorcycle away from the center of the turn.
• Stability Condition: To maintain balance during a turn, the motorcycle must lean toward the center of the curve. The angle of heel θ is determined by balancing the overturning moments (centrifugal couple and gyroscopic couple) with the stabilizing moment provided by the weight of the motorcycle acting through the center of gravity.

The stability is achieved when the net moment about the point of contact with the ground is zero. Designers often arrange the engine rotation to be opposite to the wheel rotation to neutralize the gyroscopic couple, thereby enhancing the overall stability of the motorcycle during cornering.