Introducing
Your new presentation assistant.
Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.
Trending searches
Pranav Thiyagarajan
Problem Statement
Create a stable four-legged structure for traversing a rough incline, and explore how its shape and certain factors impact it's terminal velocity.
The terminal velocity of the ramp's descent is directly influenced by the incline of the ramp, while the density and friction of the surface, along with the surface area of the ramp, play indirect roles in affecting the terminal velocity.
The structure of the legs affect the movement of the walker.
Before getting in to the answers to the questions, this is an explanatory slide to give the viewer a brief idea of the concept(s) of torque & toppling
Definition:
Torque is the rotational force applied to an object around an axis, causing it to rotate.
Torque depends on both the force applied and the distance from the axis of rotation.
Mathematically,
Torque ( ) = Force (F) × Lever Arm (r).
Toppling occurs when an object loses its balance and starts to rotate or fall.
It is influenced by the distribution of mass, base area, and the center of gravity.
A stable object has a low center of gravity and a wide base.
The walking, as we call it, is actually a step function. It is somewhat similar to an animal walking on a ramp, except the hind legs drag on.
Surprisingly so, there is not an instant where both legs are in contact with the ground! (during the movement).
The above is true because of the curved feet of the walker.
We shall go more in detail about the step function and the structure & geometry of the legs
There are two main conditions:
If the angle is too small, the ramp walker won't walk. How small? Let's explore when the walker begins to slide or move on the ramp, with the smallest angle possible.
-1
A slightly higher angle than tan will make the walker move, but anything lower will keep it still.
If the angle is too large, the ramp walker won't walk either.How large?
Let's explore when the walker begins to topple off the ramp, with the largest angle possible.
-1
A slightly lower angle than tan (b/h) will make the walker move, but anything above will result in it toppling.
sliding = walking (here)
Mass is irrelevant in all derivations; the walker's weight doesn't matter, as long as there are:
Again there would be two extreme conditions:
For the walker to move, enough force parallel to the incline must exceed the opposing friction.
There also is the possiblility of the walker toppling, just like anything with a rubber base toppling when applied with a force on the top
On a smooth incline, the walker moves uncontrollably, risking falls due to the lack of controlled sliding.
At a certain angle, the walker can move, but it won't actually "walk".
On smooth inclines, all four legs of the ramp walker will be at contact with the ground, as it slides down.
The experimental analysis will either confirm that the thesis is correct, OR, partially incorrect, or even completely wrong.
The walker "walks" a certain distance, in a certain amount of time, at a certain angle.
Multiple angles have been tested to check Questions 2 and 4 from the POI (points of importance)
Mathematically, above a certain angle, or below, the walking is NOT observed.
x-axis = TRIALS
y-axis = velocity
Mathematically, depending upon the coefficient of friction, the walker will either slide, walk properly, topple, or stay motionless.
x-axis = TRIALS
y-axis = velocity
Different surfaces are used
A generalized walker velocity is crucial, enabling future predictions without the need for time-consuming experiments.
This helps save time when determining the velocity over extensive distances covered by the walker.
We shall calculate the distance covered by ONE leg per step function.
Thesis
Result
Incline of ramp directly
increases velocity
TRUE
Density indirectly affects velocity
FALSE
Surface area of ramp is indirectly proportionate to velocity
TRUE
Friction is indirectly proportionate to velocity
Structure of legs affect the movement
TRUE