# GATE Questions & Answers of Displacement, Velocity and Acceleration Analysis of Plane Mechanisms

## What is Displacement, Velocity and Acceleration Analysis of Plane Mechanisms ?

The objective of Displacement, Velocity and Acceleration Analysis (kinematic analysis) is to determine the kinematic quantities (e.g. displacements, velocities, and accelerations) of the elements of a mechanism when the input motion is given. Identifying the displacements, velocities, and accelerations of one or more points on linkages is important in force analysis of mechanisms.

## What is the Weightage of Displacement, Velocity and Acceleration Analysis of Plane Mechanisms in GATE Exam?

Total 35 Questions have been asked from Displacement, Velocity and Acceleration Analysis of Plane Mechanisms topic of Theory of Machines subject in previous GATE papers. Average marks 1.46.

A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed, the number of links that can rotate fully is __________.

For an inline slider-crank mechanism, the length of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1 m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________radian/s.

In a slider-crank mechanism, the length of the crank and the connecting rod are 100 mm and 160 mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counter-clockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is__________

Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in figure. Link 1 is rotating at a constant angular velocity of 20 radian/s  counterclockwise. The magnitude of the total accelecration (in m/s2) of point P of the block with respect to fixed point O is___________

A slider crank mechanism with crank radius 200 mm and connecting rod length 800 mm is shown. The crank is rotating at 600 rpm in the counterclockwise direction. In the configuration shown, the crank makes an angle of $90^\circ$ with the sliding direction of the slider, and a force of 5 kN is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in kN-m) is __________

The rod AB, of length 1 m, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along QP and QR. If the velocity $V_A$ of the slider at A is 2 m/s, the velocity of the midpoint of the rod at this instant is ___________ m/s.

The number of degrees of freedom in a planar mechanism having $n$ links and $j$ simple hinge joints is

Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $\tau$ is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle , $\theta$ versus time

The number of degrees of freedom of the planetary gear train shown in the figure is

In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, the maximum acceleration of the slider (in m/s2) is _______.

In the figure, link 2 rotates with constant angular velocity $\omega$2. A slider link 3 moves outwards with a constant relative velocity VQ/P, where Q is a point on slider 3 and P is a point on link 2. The magnitude and direction of Coriolis component of acceleration is given by

The number of degrees of freedom of the linkage shown in the figure is

For the given statements:

 I. Mating spur gear teeth is an example of higher pair II. A revolute joint is an example of lower pair

A rigid link PQ is 2 m long and oriented at 20° to the horizontal as shown in the figure.The magnitude and direction of velocity VQ,and the direction of velocity VP are given.The magnitude of VP (in m/s) at this instant is

An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______

A 4-bar mechanism with all revolute pairs has link lengths lf = 20 mm, lin = 40 mm, lco = 50 mm and lout = 60 mm. The suffixes 'f', 'in', 'co' and 'out' denote the fixed link, the input link, the coupler and output link respectively. Which one of the following statements is true about the input and output links?

A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s2. When the angular velocity of the link is 4 rad/s, the magnitude of the resultant acceleration (in m/s2) of the end P is _______

A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the given configuration, the speed (in m/s) of the slider is _______

A uniform slender rod (8 m length and 3 kg mass) rotates in a vertical plane about a horizontal axis 1 m from its end as shown in the figure. The magnitude of the angular acceleration (in rad/s2) of the rod at the position shown is _______

A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1 m, the magnitude of the absolute acceleration of the block at location A in m/s2 is

A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rockerrocker) mechanism is

A solid disc of radius $r$ rolls without slipping on a horizontal floor with angular velocity $\alpha$ and angular acceleration $\alpha$. The magnitude of the acceleration of the point of contact on the disc is

In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is

A double – parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is

For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is

Mobility of a statically indeterminate structure is

There are two points P and Q on a planar rigid body. The relative velocity between the two points

Which of the following statements is INCORRECT?

For the configuration shown, the angular velocity of link AB is 10 rad/s counterclockwise. The magnitude of the relative sliding velocity (in ms-1) of slider B with respect to rigid link CD is

A simple quick return mechanism is shown in the figure. The forward to return ratio of the quick return mechanism is 2:1. If the radius of the crank O1P is 125 mm, then the distance 'd' (in mm) between the crank centre to lever pivot centre point should be

Match the approaches given below to perform stated kinematics / dynamics analysis of machine.

 Analysis Approach P. Continuous relative rotation 1. D’ Alembert’s principle Q. Velocity and acceleration 2. Grubler’s criterion R. Mobility 3. Grashoff’s law S. Dynamic-static analysis 4. Kennedy’s theorem

A planner mechanism has 8 links and 10 rotary joints. The number of degrees of freedom of the mechanism, using Gruebler’s criterion, is

The input link O2P of a four bar linkage is rotated at 2 rad/s counter clockwise direction as shown below. The angular velocity of the coupler PQ in rad/s, at an instant when $\angle$O4O2P = 180°, is

A quick return mechanism is shown below. The crank OS is driven at 2 rev / s in counter – clockwise direction.

If the quick return ratio is 1:2, then the length of the crank in mm is