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Project Pythagoras

Project Pythagoras is my third robotic prototype that attempts to further refine and explore the balance between organic evolutionary forms and engineered structures in an attempt to achieve a functional and practical bionics paradigm.

The most obvious change, other than the stylistic differences of the design, is the addition of a hollow wheel and tire that now comprises the 'foot' of the limb. This wheel is held in place by three internal rollers, much in the same way a tank tread is held in place. When the limb is fully collapsed, as shown in the above image, these wheels are free to rotate leaving about two centimeters of clearance off the ground. Thus, they are excellent for moving on relatively even or smooth surfaces commonly found in urban environments. This is known as Drive Mode.

As the machine is given a command to extend the leg, two talons at the tip come under the wheel and raise it off of the ground. The robot has now transitioned into Walk Mode. Now it may be programmed to commence quadrupedal locomotion using the two motors in each limb to control the forward/backward and expand/contract movements associated with walking.

Three external plates add extra protection to the limb's internal mechanical components. Each of these plates is supported by a reinforced back plate, and can be easily removed and swapped out in the case of damage with only a few quick steps. The two topmost plates are designed to slide in and out as the leg expands and contracts, thus keeping the machine's profile as slim as possible while in Drive Mode.

As is the case with my previous two prototypes, Pythagoras is constructed from laser cut sheets of Delrin acetal homopolymer resin. This material is a favorite of mine, as its physical properties mimic that of organic bone in many parameters, yet it is lighter, relatively chemical resistant, and infinitely easier to shape and form.

Each leg is constructed with over 40 individual components, nearly all of which are laser cut from flat sheets of Delrin. Parts produced in this manner are vastly less expensive compared to those created from many other manufacturing methods. It is my goal to make functional robots that are both affordable, and expendable.

Two stepper motors are used to control the horizontal and vertical movements of each leg. The rear two legs of the machine would contain an additional motor for powering the rear wheels when in Drive Mode. Stepper motors are a promising, and relatively new motor technology that have many characteristics well suited for robotics. They can be programmed to make precise movements, and exhibit a surprising amount of strength for their size.

Much like the anatomy of an organic quadruped, each segment of the limb is composed of several thin and flexible struts. Every area critical to the structure of the leg has at least two of these struts to ensure that in the event one is broken, the machine will still be able to stand, and perform its objectives without needing immediate repair.


To give a more complete perspective on what the full PYTHAGORAS prototype would look like, I have rendered several additional images showcasing the full range of functions and motions that could be possible with such a design.

With all four legs in place, the machine now resembles a more familiar quadrupedal form. Though unlike most quadrupeds, it does not feature a typical hind leg - opting for a more symmetrical configuration. This is advantageous for several reasons, the first of which being that the lack of dedicated hind legs would lessen the number of variables in programming a walk cycle, and the second being that the machine does not have to turn around to reverse its direction.

With a height of only 20 centimeters while in Drive Mode, the machine has an extremely low profile. This makes it optimal for squeezing into tight maintenance areas, sliding under raised surfaces, or for storing in places where saving space is critical.

Turning can be accomplished via two axes of rotation located within the central mass of the machine. These points of articulation would be effective for both Drive and Walk Modes.

Because each leg uses an independent motor to control the horizontal movement, one rather interesting aspect of the prototype is the ability to extend or contract its limbs on demand. By manipulating this motion it would be possible to make the machine 'crawl' using only limited motor functionality.

With its legs extended into Walk Mode, the prototype has more than enough clearance below its central mass to climb up or over many small obstacles relative to its size. Ideal for moving over uneven terrain, this mode would be more commonly used for non-urban environments.

With two independent motors used in each limb, a large range of movements can be programmed. From small, careful 'tiptoeing' to fast moving jaunts, the system is limited by design to allow only for articulation relevant to locomotion, and nothing more.

It is a daunting task to come up with ideas for making a functional and practical robotics design. However, I find that working off of natural systems - systems that have proven their effectiveness with millions of years of evolution to develop them; are a better starting point than any. For it is my belief that the roboticist is not merely a person attempting to replicate the wondrous multitude of natural processes found in life, but rather one who seeks to understand life on its most fundamental, and extraordinary level.


- Christopher Nicholas Capen