Question

2 The figure shows a mechanism consisting of a slider, attached to link 3 at B through a revolute joint. Link 3 is attached to link 2 through a revolute joint at A. Link 2 is attached to the inertial frame through a revolute joint at O. Link 2 is 200 mm long and link 3 is 300 mm long. B is constrained to move in a slot angled at 40° to the horizontal. Initially, B is horizontally in line with O and is at rest. At this point, the distance between O and B is 250 mm. B then accelerates at a rate proportional to the velocity according to the equation a-kv where k 10 s1 After the slider has moved a distance of 100 mm determine its velocity At this point determine the velocity of A and the angular velocities of links 2 and 3 using: 1. Graphic methods (choose a scale such that the length of the velocity vector for B is 5 cm) 2. Vector Methods 3. Instantaneous centre of zero rotation At this point determine the acceleration of A and the angular accelerations of links 2 and 3 using- 4. Graphic methods (choose a scale such that the length of the acceleration vector for B is 5 cm) Vector Methods 5.

Answer 1

Answer:

Question A:

Graphic Methods:

Graphical method starts with position analysis by simply drawing the linkage mechanism to scale. Then the velocity analysis is performed which requires the angular position of the links to be determined beforehand. Similarly it is necessary to know angular velocities of links for acceleration analysis. Thus, the sequence for kinematic analysis of mechanisms is – position analysis, then velocity analysis and then acceleration analysis.

Different Techniques of Graphical Analysis

1. Velocity and Acceleration Polygon: Velocity and acceleration are vectors and thus their sum or difference will follow vector polygon laws. If velocity of one point on a link is known then the velocity of other points can be found using the vector polygons. This technique is based on vector polygon laws.
2. Velocity and Acceleration Image: This technique is used for graphical analysis of mechanisms with more than one loop. If the velocity and acceleration of two points on a link are known then the velocity and acceleration of third point on that link can be determined using velocity and acceleration image.
3. Inversion Technique: When it is not possible to analyse the linkage directly using vector polygon approach then Inversion Technique is used. In this technique the driven and driver cranks are interchanged to perform graphical analysis.
4. Relative Velocity and Acceleration: This technique is used to analyse mechanisms with large number of members. In this technique the relationships between relative linear/angular velocities and acceleration of points/members are used to analyse the mechanisms.
5. Instant Center of Velocity: For a rigid body moving in a plane, at every instant there exists a point that is instantaneously at rest. This instant center of velocity for the given rigid body is found using standard methods. It is useful for finding input-output velocity relationships of complex mechanisms.