Plane Curvilinear Motion: x-y Coordinates - Example Problem 3.1-6

 

The carriage, shown in the figure, has a vertical slot that is driven in an oscillatory manner. The carriage’s horizontal position as a function of time is x = 3sin(2t), where x is in cm and t is in seconds. This carriage in turn drives the motion of pin A which is further constrained to move in the parabolic slot whose shape is described by the function y = -x², where the y coordinate also has units of cm. Determine the overall velocity of pin A as a function of time.

 

 

Given:

• x = 3 sin(3t)
• y = -x ²

 

Find: v

 

Solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

What is the position of pin A?

 

r = 3 sin(2t) i - x² j cm
r = - x² i + 3 sin(2t) j cm
r = 6 cos(2t) i - 2x j cm