GATE 2024 Mechanical Engineering: Important basic concepts in Theory of Machines/Dynamics of Machines (Mechanical Engineering) for GATE 2013

This article deals with common basic concepts to keep in mind the theory of machine/Dynamics of Machine subject.

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A kinematics chain needs a minimum of 4 link and 4 turning pairs.
If the frequency of oscillation on earth is n then the frequency of oscillation on the moon will be n/√6.
The total number of instantaneous centers for a mechanism of n link is equal to n(n-1)/2.
In the case of an elliptical trammel, two pairs turn, and two pairs slide.
A shaft revolving in a bearing forms a lower pair.
For kinematic chains formed by lower pair the relation between the number of link L and the number of joint J is given by L = 2/3 (J+2).
The mechanism used to enlarge or reduce moments for reproducing drawings to different scales is called a pantograph.
The number of links in a pantograph is 4.
If a link has a velocity that changes both in magnitude and direction at any instant, then it must have two components of acceleration e.g., centripetal. And tangential.
The Klein’s method of construction for reciprocating engine mechanism utilities a quadrilateral similar to the diagram of a mechanism for the reciprocating engine.
In elliptical trammels have two pairs turning and two pairs sliding.
When a ship travels in the sea, the effect of the pitching is more dangerous.
If ф is the angle of friction, the limiting value of tan ф will be µ.
Multiple collars are provided on a flat collar pivot bearing to distribute the axial load due to limiting bearing pressure on a collar.
Slip in belt drive is different between the linear speed of the rim of the pulley and the belt on it.
In the case of flat belt drive the length of the belt in case of gross belts depends on the sum of the diameters of pulleys.
A pantograph is a mechanism having lower pairs.
Kinematic pairs are those pairs that have two elements that allow relative motion.
A cam with a roller follower would constitute a higher pair.
Peaucellier mechanism has eight links.
Hart mechanism has six links.
For a kinematic chain to be considered as a mechanism one link should be fixed.
The cam angle is the angle of rotation of the cam for a definite displacement of the follower.
Klein’s construction is used to find out the acceleration of various parts.
For stable governor, there is one radius of the governor weight for each equilibrium speed.
In the case of a governor isochronous is only one equilibrium that is constant for all radii of rotation of the bells within the working range.
The module can be expressed in mm.
The bipolar suspension method I used to find out the moment of inertia.
Instantaneous center of rotation of a link in a four-bar mechanism lies on a point obtained by the intersection of extending adjoining links.
A reverted gear train is one in which the first and last gear are on the same shaft.
In the case of spur gears, the flank of the tooth is the part of the tooth surface lying below the pitch surface.
In the case of a cross helical worm, the axes of two shafts are non-parallel-non-interesting.
In the case of gears, the addendum is given by one module.
Gears for watches are generally manufactured by stamping.
A cam wherein the follower reciprocates or oscillates in a plane parallel to the axis of the cam is called cylindrical cam.
Rope break Dynamometers uses no lubricant.
Tesla fluid friction dynameters used for power measurement when the speed is high and the viscous force is small.
Hydraulic Dynamometers is widely used for absorption of wide range of power at a wide range of speed.
The secondary disturbing force because of inertia of reciprocating mass is given by W/g ω² r/n cos θ.
In a balancing machine the units for unbalance measurements are gm-cm.
In a Hartnell governor if the stiffness of spring is increased the governor will become less sensitive.
The supply of working fluid to the engine to suit the load conditions can be controlled by the governor.
The governor used in gramophone is of pickening type.
A porter governor could be classified as dead weight type governor.
The function of a governor is to adjust variation of speed by varying the input to the engine.
If D and T be the pitch circle diameter and no. of teeth of a gear, then its circular pitch p = π D/T.
If D₁ and T₁be the diameter and no. of teeth of gear 1 and D₂ and T₂ the corresponding value of other gear in mesh, then ratio N₁/N₂, will be equal to D₂/D₁.
A scott-russel mechanism is made up of sliding and turning pairs.
Ackerman steering gear is made up of turning pairs.
A sliding crank chain is made up of three turning and one sliding pair.
A motor car takes a bend of certain radius in right-hand direction when moving at some speed. If engine rotates in a clockwise direction when viewed from front, then because of centrifugal force reaction on the outside wheel is increased and on inside wheels decreased.
If δ be the static deflection of shaft under the gravity load, then natural frequency of the system in case of the longitudinal and transverse vibration is equal to 1/2 π √g/δ.
Cold working increased the fatigue strength.
Coaxing is the procedure of increasing fatigue limit by overstressing the metal by successively increasing loadings.
The notch angle of the Izod impact the test specimen is 45⁰.
In vicker’s hardness testing, the pyramid indentor apex is 40⁰.