The Assignment:
Before beginning work on our Lego race cars, the class was instructed to investigate different kinds of mechanisms and how they convert one kind of motion into another, and more specifically how linear rotation can be converted into rotation motion and vice versa. In order to investigate these mechanisms we explored the Cornell's KMODDL or Kinematic Models of Design Digital Library. http://kmoddl.library.cornell.edu/index.php
Reciprocating Rectilinear Motion:
The mechanism which I found to be most compelling was the reciprocating Rectilinear Motion design. It's design is a compact and ingenious way to convert rotational motion to linear motion. A video of this mechanism is linked below.
How It Works:
The Reciprocating Rectilinear Motion Mechanism utilizes the relationship between simple harmonic motion that connects constant rotational motion to that of springs and linear motion. Ideal friction-less springs can be used to interpret this kind of motion through the equations F = kx (where F is the force on the mass of an object, k is the spring constant and x is the distance from the equilibrium position) Since F = ma we can derive the acceleration of the spring. Thus a =(kx)/m As a consequence of this, As the mass approaches the equilibrium position the speed increases until it reaches its maximum through the equilibrium position, As the mass gets closer to the maximum displacement position the velocity approaches zero and instantaneously goes to zero before changing direction. This motion is pictured below is known as a linear restoring force.
The Reciprocating Rectilinear Motion Mechanism uses this mathematical relation ship and takes it one step further by incorporating a gear system that converts the linear motion contrived from the simple harmonic nature of the rotational motion and then converts that motion into another linear motion perpendicular to the other. The partial gear at the bottom has the same radius of curvature as the wheel above allowing the lateral piece to move with a 1:1 ratio.
Potential Applications:
This kind of mechanism would be useful for something that wants to convert a constant rotational velocity of the disk to a varying linear velocity that reaches its maximum at the linear portions highest displacement. Things such as variable speed saws, that need to accelerate quickly upon each stroke would require this kind of mechanism.
How It Works:
The Reciprocating Rectilinear Motion Mechanism utilizes the relationship between simple harmonic motion that connects constant rotational motion to that of springs and linear motion. Ideal friction-less springs can be used to interpret this kind of motion through the equations F = kx (where F is the force on the mass of an object, k is the spring constant and x is the distance from the equilibrium position) Since F = ma we can derive the acceleration of the spring. Thus a =(kx)/m As a consequence of this, As the mass approaches the equilibrium position the speed increases until it reaches its maximum through the equilibrium position, As the mass gets closer to the maximum displacement position the velocity approaches zero and instantaneously goes to zero before changing direction. This motion is pictured below is known as a linear restoring force.
If the displacement of the mass on a spring can be represented mathematically as a sine curve which is derived directly from a circle. As we can see from the picture below, the displacement of an object form the x axis follows the circumference of a circle.
The Reciprocating Rectilinear Motion Mechanism uses this mathematical relation ship and takes it one step further by incorporating a gear system that converts the linear motion contrived from the simple harmonic nature of the rotational motion and then converts that motion into another linear motion perpendicular to the other. The partial gear at the bottom has the same radius of curvature as the wheel above allowing the lateral piece to move with a 1:1 ratio.
Potential Applications:
This kind of mechanism would be useful for something that wants to convert a constant rotational velocity of the disk to a varying linear velocity that reaches its maximum at the linear portions highest displacement. Things such as variable speed saws, that need to accelerate quickly upon each stroke would require this kind of mechanism.
Hi Izzy! Your post was very well researched and it was clear you put a lot of thought into how your mechanism worked. I especially enjoyed the pictures you attached to your explanation. It helped make the post very clear.
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