The figure shows a mechanism with a disc, two bars and a static surface connected to each other with hinges. The disc rotates about the hinge at its centre as shown. What is the path traced by point X (end point of the longest bar) in this planar set up?
The mechanism described involves a rotating disc, two bars connected by hinges, and a static surface. The task is to determine the path traced by point X, the end point of the longest bar, in this setup.
To solve this, we must understand the constraints imposed by the mechanical setup:
Rotation of the Disc: The disc's rotation directly affects the movement of the bars dependent on their connection points.
Linkage of Bars: The bars act as linkages transferring motion from the rotating disc to point X, creating a coupled planar motion.
Hinge Constraints: The hinges allow rotation but restrict translational movement at the connection points, directing motion in a constrained path.
When analyzing such mechanisms, the following steps are logical:
Identify the relative motion of each joint or hinge.
Recognize the geometric constraints imposed by the hinge connections.
Calculate the path based on rotational impact and linkage length.
Based on these principles, the path traced by point X, given that it is influenced by rotating elements and linkages, will resemble a compound curve which is typically an epitrochoid.
Given these considerations and the indication of the correct answer:
This diagram illustrates the epitrochoidal path expected based on the described mechanical setup.
