Engineered jumpers overcome biological limits via work multiplication
"Work multiplication" allows engineered jumpers to store significantly more energy in springs than biological ones, enabling extraordinary jump heights. This post tells the story of our record breaking jumper and the development of the concept of "work multiplication."
“Is that the highest it can jump? Can I build something better?” These are the questions that begin two pivotal chapters of our quest to build the world’s highest jumping jumper.
About seven years ago, well before my involvement in the project, the inklings of our journey began with Morgan, then a graduate student along with Elliot at Stanford. Fresh off a project involving a robot that could both jump and fly, he wondered how high can a pure jumper jump? And like his predecessors, he ran the calculations and found the numbers astounding. Simple physics models predict heights well over 100 meters. Extraordinary numbers demand extraordinary proof. Seeing is believing.
For a quick test, Morgan assembled a prototype with a scrap carbon fiber rod, washers, duct tape, and lots and lots of rubber bands, because rubber bands have high specific energies. To the astonishment of Elliot and Morgan, “it went up forever” into the evening sky, 8-10 m, nearly the height of their building. Even though it was a manually loaded stick-looking contraption with rubber bands (affectionately dubbed Stick-bot), it showed promise.
But then graduating, theses, jobs, and life got in the way. However, such questions are beguiling. You see elastic jumper after elastic jumper clear about 3-4 meters and think: is that the highest elastic devices can jump? Can I build something better? How hard can it really be? After about a year and half of wondering, Elliot approached Morgan, who was then working at Disney with Günter, on a proposal to go for a world record.
Besides the fun element, this collaboration made sense. At the time, researchers at Disney were exploring ways to launch stunt-double robots.
The establishment of the collaboration resulted in a flurry of prototypes between Elliot and Morgan. They focused on lightening the supporting structures for the rubber bands, designing a motor and gearing that could stretch the bands, and a mechanism to rapidly release the energy. Designs ranged from structureless (i.e., using the surrounding environment, such as a stop sign, as structure) to ones using aluminum, paper, carbon fiber, etc.
While there is an excitement to developing new ideas, it is important to not get bogged down by the minutia. During this time, Günter kept the group focused by emphasizing the physics, not the specific mechanism or design. Ultimately, the emphasis on the science led us to our first energy model and a jumper that reached 12 m, which exceeded the best elastic jumpers (~4 m), and even broke the world record for any jumper, set previously by a compressed-gas device that reached 10 m. However, the model also told us that despite the impressive jumps, our devices at the time fell well short of the theoretical limits, even with losses accounted for.
To address the shortcomings, we began using carbon fiber bow springs instead of rubber bands. Although carbon fiber in bending has lower specific energy than rubber in tension, it reduces the need for a supporting structure, allowing our jumpers to have better overall specific energy.
COVID-19 accelerated development. The jumper became our pandemic project, our sourdough bread. Bored at home, Richard greatly increased his involvement. He spent hours at home over the spring and summer iterating, eventually building one that jumped over fifteen meters. During the fall, Elliot took over, and after countless hours in his garage, brought the jumper to twenty-six meters. At that point, we knew we had something special. Led by Elliot and Günter, we began drafting a paper and by December we submitted it.
The reviewers were not convinced. Although they admired the engineering achievement, they felt that the paper did not offer new understanding. Besides jump height, what new insights did we bring? We reexamined our model and realized that at a high level it stated the obvious: reduce losses.
After mulling over the reviews and reading through countless papers on jumpers, most of which were exclusively about biological ones, we realized there was an intriguing, seemingly unanswered question, which was a variant of our original motivating question: “What are the limits of jump height and how do they differ for biological versus engineered jumpers?” The team realized we needed a completely new model to answer this question—instead of describing the energetic losses during a jump, we needed to know the limits of energy production before losses occurred. To help create this new model, I was brought onto the team.
Simultaneously, the jumper problem captivated Chris. Every spring quarter, Elliot teaches the junior design class and challenges the students to build a jumper from rubber bands, some wooden dowels and popsicle sticks, a tiny motor, and a 9V battery. While many students just wanted to get off the ground, he wanted more. The simplicity of the problem fascinated Chris. He spent hours and hours fine-tuning his design; eventually, he shattered the class record, jumping over five feet high.
At the end of the assignment, Elliot showed a video of his carbon fiber-based jumper, and Chris felt the same compulsion to answer the questions: is that the highest it can jump, and can I build something better?
After talking to Elliot about it, Chris convinced Elliot to let him work on the jumper. And that is one of the unique things about the Hawkes Lab: we allow and encourage undergraduates to make significant contributions. He quickly replicated Elliot’s jumper and began working on a new one.
Now we sought to go higher. With our new model, we identified a key difference between engineered and biological jumpers: “work multiplication.” Biological jumpers have a fundamental limit on energy production set by the work they can produce in a stroke of their muscle; but engineered jumpers can “multiply” the work they can do in a single stroke. Rotary motors and ratcheting allow engineered jumpers to do multiple strokes, resulting in large energy production.
This difference offered key insights for design. First, to maximize jump height, engineered jumpers of moderate scale (30 cm) should use latched springs to store the vast amount of energy, whereas biological jumpers of the same scale should not. Second, engineered jumpers should maximize the specific energy of their spring, whereas biological jumpers should maximize the specific energy of their motor (muscle). Finally, engineered jumpers should have a spring-to-motor mass ratio that is much, much larger than ideal for biological ones.
So, we returned to the design, looking to maximize spring size and specific energy. Chris, only two months in, proposed a new concept of adding high specific energy rubber to the current bow springs to boost overall specific energy. Matt modeled this new idea, and sure enough, the specific energy was predicted to be nearly 20% greater than any previous design. And furthermore, Matt discovered that the arrangement Chris proposed should decrease peak stress in the carbon fiber, allowing larger bows and increasing not only spring specific energy but also the spring-to-motor mass ratio.
About two months later, on a clear day out on the bluffs overlooking the Pacific Ocean, Chris tested the new design, and measured a seemingly infinite hangtime of over 5 seconds. He had just set a very high bar: 32 m.
The improved jumper combined with months of writing resulted in a completely reworked paper, which was ultimately accepted. We want to thank the reviewers and editors for pushing us to truly examine our contributions and for providing thorough and helpful critiques.
Yet again, I am reminded that simple questions lead to profound findings both in science and in life. I encourage readers to put on some safety glasses and give it a go. Beat our jumper. Building a record-setting jumper requires no special tools and materials or advanced physics knowledge. Who knows what you will learn?