Relative velocity method_01
- 1. A four-bar mechanism with dimensions as shown in the figure, is driven by crank 2 at constant angular speed of 600 rpm CCW. Find the instantaneous velocities of coupler P and linear velocities of links 3 and 4 in the position shown. Solution: (a) Solve for the linear velocity of crank 2 J J I $ $ { I { F % % J J I J I (b) Drawing the link using CAD: (c) The vector equation connecting known velocity vB to unknown velocity vC on the same link BC is: - È (d) Sketch the velocity polygon, (scale 1:10) Select suitable position of pole OV, draw the first velocity vector VB, considering its magnitude and direction. Sketch velocity vC from OV, knowing only its direction, which is perpendicular to crank DC. Finally, sketch velocity VC/B from the tip of VB, the direction of VC/B is perpendicular to link BC The intersection of OvC and bc is the magnitude of each velocity: {% %% {{ { % %% and È {% %%{{ { % %% . (e) To obtain linear velocity of point P, we will use the principle of velocity image.
- 2. From b, draw line bp, in the direction perpendicular to the line joining BP. Similarly, from c, draw a line cp, in a direction perpendicular to the line joining CP. The intersection of the two lines define velocity image of p of coupler point P. It can be verified that triangles BPC and bpc are similar. Line OVp on velocity polygon represents velocity vP of couple point P. The sense of vP is decided by referring to the velocity equation: - È The magnitude of velocity P is: { %{{ { % Summary of Answers: YV X YV X Y X Reference: Mechanisms and Machine Theory by Ashok G. Ambekar © 2007 by Prentice Hall of India Private Limited, New Delhi