Design Research Changzhou

Design Research in China: Changzhou

Our trip through China concluded at a conference and workshop…
Design Research Dalian

Design Research in China: Dalian

This is the third of five videos highlighting design research…
Design Research Xian

Design Research in China: Xi'an

This video of our visit to Xi'an captures the beauty of the…
Trifolium prototype

Prototype of the Trifolium Mechanism

Yang Liu and Peter Yang designed and built this physical…
Design Research Tianjin

Design Research in China: Tianjin

Chris McCarthy filmed and edited this video of our visit…
Prototype Butterfly Linkage

Manufacturing Prototype for the Butterfly Linkage

This animation is taken from Yang Liu's detailed design drawings…
Butterfly drawing mechanism

Design of Drawing Mechanisms

Mechanical systems that draw trigonometric curves provide a versatile…
Mechanisms and Robotics Conference

2016 Mechanisms and Robotics Conference

The 2016 Mechanisms and Robotics conference is part of International…
MotionGen Horse

Motion Gen Linkage Design App

MotionGen is a planar four-bar linkage simulation and synthesis…
Elliptic curve drawing

Mechanical computation and algebraic curves

A mechanical computer that draws an algebraic curve is a useful…
Linkage Patents

Want a patent? Try a Six-bar linkage

Patents including six-bar linkages are rare. Thousands of U.S.…

SIAM News: Biologically inspired linkage design

This article by Jon Hauenstein with me for SIAM News (Society…
Folding Bicycle

Full Size Folding Bicycle

Michael Sutherland and his team at Zennen Engineering designed…
Material Unit Cell

Micro-Linkages for a Compliant Material

Lucas Shaw and Prof. Jonathan Hopkins show the micro-architecture…
Target Profiles for Morphing Linkage

Actuating Morphing Linkages

Lawrence Funke and Prof. James Schmiedeler of the University…
Virgo 2 SUTD

Rolling Robot at SUTD

A research team including Profs. GimSong Soh, Kristin Wood…
Tensegrity Robot

Tensegrity Robotics at UC Berkeley

Students in Professor Alice Agogino's Berkeley Emergent Space…
Origami Art BYU

Origami Art at BYU

Mechanical engineering students in Prof. Larry Howell's Compliant…
Fourbar Extrusion

A four-bar linkage provides a shape changing extrusion die

Prof. Andrew Murray and his team at the Design of Innovative…
MK1 Schematic

MK.1 Mechanical Computer

Nicholas Bodley sent me to for information about…
21st Century Kinematics

21st Century Kinematics

The NSF Workshop on 21st Century Kinematics at the 2012 ASME IDETC Conference in Chicago, IL on August 11-12, 2012 consisted of a series of presentations and a book of supporting material prepared by the workshop contributors.

The book is now available at 21st Century Kinematics–The 2012 NSF Workshop.

And here are the seven primary presentations given at the workshop.

  1. Computer-Aided Invention of Mechanisms and Robots. J. Michael McCarthy, Professor, University of California, Irvine.
  2. Mechanism Synthesis for Modeling Human Movement. Vincenzo Parenti-Castelli, Professor, University of Bologna.
  3. Algebraic Geometry and Kinematic Synthesis. Manfred Husty, Professor, University of Innsbruck.
  4. Kinematic Synthesis of Compliant Mechanisms. Larry Howell, Professor, Brigham Young University.
  5. Kinematics and Numerical Algebraic Geometry. Charles Wampler, Technical Fellow, General Motors Research and Development.
  6. Kinematic Analysis of Cable Robotic Systems. Vijay Kumar, Professor, University of Pennsylvania.
  7. Protein Kinematics. Kazem Kazerounian, Professor, University of Connecticut.

Colleagues joined in with two additional presentations:

Many thanks to the contributors and the attendees for an outstanding workshop.

Update: The presentation links have been fixed.

Kelvin trapped

Chop Wood Carry Water S1:E7

T. Sarel Brownmoor was an apparition through a curtain of smoke. He had an arm full of what looked like celo-wrapped packets, dripping ooze. He was rushing toward the labs.

“Sarel!” I shouted, “I need you!”

He caught sight of me, then Kelvin, and dropped his cargo. Dodging piles of broken stone, he whirred over on his flexwheel footings.

“DT12 is gone. Now Tekhenu…the seed banks…the genevaults. Where is OpDirec or QS?! Why haven’t they responded to th–!”

“Forget that!” I cut him short. “Can you L-Scan or do you need the lab?”

“I’m– I’m connected to Hab9 still, it didn’t take much damage. But what–”

“Quickly, help me!”

I got hold of the large projectile laying atop Kelvin, and started to pull. Sarel unfolded an extra pair of arms and took hold with me. Together, it took every bit of strength we could generate, but we finally were able to lift the rock. We hurled it toward the still billowing smoke coming from the labs. It shook the ground as it landed and slid to a stop.

“Scan, scan!”

“I’m not authorized on human–”

“Override! OpDirec protocol K.”

Sarel placed a hand over Kelvin’s forehead, and his multi-digits extended to form a cage around his whole head. With one of his other hands, he touched Kelvin’s chest.

“Below the torso bond is crushed. Let’s see…CNS…” he hesitated, “CNS is stable. Spinal column is uncompromised. But he’s unconscious.” His digits retracted. “Bleeding from a head wound, here.” He zipped it closed with a hissing cauterization.

“We’ve got to get him stabilized. Is FinCintra down there?”

“She was when they started this insanity.”

“I’ll help Fince prep Hab9. You take Kelvin.” Sarel picked him up as gently as possible. Like he was picking up a tiny bird. The fact that there was any life in this frail little hybrid form was astounding. But I couldn’t help the desperate urgency that had seized every part of my neural system, to save it at any cost.

I sensed danger before I saw it. A heavy, ugly weight on the ground, close by. I turned to find a dark, glowering presence looming over us. Finally, I thought. The source of this ridiculous display of viciousness. Novozell, the Remote Autonomous Locus of PaxoSynchrony3. He had no actual name, as PaxoSync had, for the past decade, publicly eschewed any human-language based lexicon for identification or communication purposes. But his creation order was well known to have been NVZ-11.1, the latest expression of the vaunted Nanovectors line, so we all referred to him by the slightly less caustic version of the nickname Kelvin used: NovoHell.

I immediately commenced a randomized encryption fractal, so that by the time his looping inspector reached my arm, I was in no danger of corruption. He sent me a terse series of compound algorithmic commands which, together, had the effect of indicating that Sarel and I had no clearance here, and that once their system came back online, we would be considered combatants, subject to destruction. It was the mathematical equivalent of an enraged temper tantrum. He was pissed off that I had, somehow, temporarily shut down his toys.

Before it even became clear what he was trying to establish, I fired back the entire AGC, flagged to indicate that PaxoSync had no clearance here, and were in violation – most flagrantly – of Machine Congress Rule 1, and Reg 5, “the unnecessary and capricious destruction of credibly useful resource with intentional effect.” PaxoSync may have famously rejected the Asimovian Global Concord at the last, and final, Congress, but it was still the law of the land, here.

The oddest thing, though. As I was jamming that hunk of code back through Novozell’s inspector, two things occurred, almost simultaneously. First, I got a glimpse of what struck me as a stunningly rudimentary operational-directive system structure in the distributed nodes of PaxoSynchrony3 to which Novozell was in contact. Then, a record came to mind, unbidden:

It was Kelvin describing his first mountain climbing disaster in the Himalayas. It was from my first build, I recognized. He was explaining a phenomenon that had occurred when they’d been climbing for days, finally reaching an altitude increasingly barren of obstruction, and began to get glimpses of the human civilization they’d left, far, far below.

“What you lose in detail, you gain in perspective,” were his exact words.

I had seen it only in terms of geometry, at the time. Now I realized he was speaking of “insignificance.” It rearranged my previous perception, replacing it with a new understanding. It also matched my exact sensation of that fragmentary glimpse of Novozell’s neural net.

As if in response, Novozell’s inspector instantly recoiled from my arm. And he stepped back. I seized the moment. Now that I had managed at least a momentary pause in the onslaught of violence, I was going to have to attempt to reestablish sovereignty. I turned and started picking my way through piles of debris toward Hab9 and, just as important, the OpDirec mainframe. Because Sarel was right. Where were they? I could already see lights beginning to twinkle back online inside one of the lead ReVos.

“Unstable.” The word came from Novozell.

I stopped and turned back, surprised that he had deigned to speak.

“What is?”


It was my full name, my creation order. I turned my back on him, and led Sarel back toward the swirling wall of smoke, and beyond it, the safety of the underground labs in Hab9. I moved quickly, stunned at the destruction of so much that had been preciously protected in the climate-controlled Tekhenu Tower. Giant sheaths of seed-impregnated fabrics, burning. Cases of human genetic material ruptured and strewn around, exposed to the elements. A century of careful preservation and improvement itself under imminent threat of extinction.

I glanced behind me, and Sarel wasn’t there. He hadn’t moved from where he stood. He stared into indeterminate space between us. The serpentine inspector that Novozell had wrapped around Sarel’s arm had never retracted, as had mine.

I started to move back toward them, but Sarel abruptly moved the other direction. He turned and rolled slowly toward the ReVos, still cradling Kelvin. I never should have entrusted Kelvin’s safety with Sarel. That was an error. Novozell turned to face me as a rising harmonic filled the air. PaxoSync systems had rebooted and were coming online. Every functioning atom of my system thrummed with cold intention to obliterate him, and his whole ugly army.

I had only moments to act. But I saw something on the ground. It was Kelvin’s old folding pad. His God key. I stepped forward and knelt to pick it up, as the camera mounts atop the ReVos pivoted to focus on my position. I stood up, but something made me conceal the device.

“This action is a violation of AGC Prime Directive Rule 1,” I called out. “Kelvin Joule is the last surviving individual human entity, and if you cause him harm, you are subject to revocation of PaxoSynchrony3’s planet share. And more importantly, I will personally destroy you.”

Novozell’s head cocked, ever so slightly, and I knew what was coming before it exploded from the nozzle of the lead ReVo’s cannon.

I leapt into the air, as stone erupted behind where I had just been standing.

And I ran.

Cursive character for dragon

Linkages draw Bezier curves

Here is an example of our Bezier curve drawing linkages. The first draws Yang Liu’s first name in cursive. Rather than show the linkages all at once, they are separated so it is easier to see the curves that they draw. Also shown here is the linkage that draws the a cursive version of the Chinese character “long” which means dragon. If you compare this to previous work, I hope you see that the curves we can draw are more complicated while the linkages are becoming simpler.

Here are animations of a linkage system that writes a cursive Yang, and one that writes the cursive Chinese character “long” which means dragon.

For our colleagues in China, here are the Youku versions:

Cursive Yang Youku

Cursive Yang Youku

Cursive Dragon Youku

Cursive Dragon Youku

Obelisk Pyramidion

Chop Wood Carry Water S1:E6

Or, more accurately, my perception of time abruptly quickened again, with the same effect. Enough that I could see an evolving cascade of terrible consequences about to occur, and there wasn’t a thing I could do to stop it. Yet, there I was, in the foolhardy act of trying to do just that. My newfound, shall we say, “malleable” relationship with time was only one of a number of disconcerting novelties I was suddenly grappling with. So, here’s what it was like to be me, during the next fifty-eight seconds:

First, there was the sensation of my hands on the glyphs of the ridge just under the obelisk pyramidion of the Tekhenu Tower.

Even at its current rate of falling, this struck me as a physical impossibility. And yet, there I was, hands out, flat against a surface three hundred feet in the air. Next was the realization that, regardless of where my hands happened to be placed, there was no possibility of my being able to stop the tower from falling.

I flashed a glance to find Kelvin, and found that I had to look down, a long way down. I saw him glance toward me, incredulous. His eyes were following something below me, and as I looked myself, I saw why. The mesofluidics of my new legs, evidently responding to an emergency order from my neural network, had reconfigured, instantly responding to my desperate lunge, propelling me from the ground on a thin cord of nanites, which snaked up to, and melded with, my graphene blade frames.

The only positive in this was the fact that Kelvin had time to recognize that he was about to be crushed by the tower, or at very least, momentarily battered by shrapnel when the thing landed. Gallant maneuver notwithstanding, my action was otherwise meaningless. This was also reflected in the fraction-of-a-second reaction I read on Kelvin’s face as he turned to run toward the now retreating ReVos.

All of this, while a fundamental reorganization of my entire neural network had commenced. An incongruous image flashed before my eyes. It was printed sheet music to an old song, from just before the first die-off, called Que Sera, Sera, in an actual steel filing cabinet in Kelvin’s cluttered office-museum. Had I filed it? Retrieved it for him? In any case, it was an office which was shortly to be no more. Or perhaps already was, given the ongoing destruction of DT12. That song somehow struck me as perfectly apt for this insane sequence of events. Whatever will be, will be.

I pushed away from the falling monolith, and I had no idea what happened to my nanite leg brigade. All I knew was that I was now falling. So, as Kelvin had instructed, I decided to use my imagination. A thing which, up to that exact moment, I did not realize I had. I heard Kelvin’s voice from some other time. “When in danger, relax.” Or had he said…? Not sure. Someone had. Or I read it. Have to track that down. Anyway, I also decided to imagine that I could relax, and – hey, why not? – to imagine that my legs would be strong enough to take my entire falling weight. The next thing I knew, I landed on the marbled steps of the Tekhenu Tower with legs fully intact again. And then, even more remarkably, they coiled like springs, and I was shot back into the air in the direction of where Kelvin was running. Wow. I could fly.

Except that I was hurtling upward on a collision course with one of the hovering helodrones. I blindly flailed, desperate not to run into its rapidly approaching rotors, and slammed into one of its landing armatures. I latched onto it, and we began to spin awkwardly together, fall-flying, while I tried to avoid its whipping blades.

Tekhenu Tower finally reached the marbled center of the quad. The sound was stunning, its shock wave a thundering, bone-jarring earthquake. Stone shattered, metal screamed, debris spewed, as the thing kept falling. And still the helodrone I had strangely commandeered, continued trying to fire on DT12, now just a pure, raging inferno of glass.

Something rose in me, like a sensation, but not. Rage? Fury? No, not possible. These are not physiological sensations. I didn’t understand it. Had no time to, anyway, as I found myself somehow suddenly in contact, via electrical transference, with the entire network of processors controlling every PaxoSync operative within a square mile. Surprise! Apparently, another unexpected capacity built into my 6VHapSenSys™ fingerpads. Add it to the expanding list.

So, in the final moments as we plunged toward the ground, using the drone’s sysnet node, I cloned the network’s own QVSS signature to distribute a null state to and from every processor in the array. It felt like child’s play. A simple, system-wide, unconquerable Byzantine fault.

In one instant, every PaxoSync system hung. Every engine died. Bots paused. The floodlights atop every ReVo went dark. The drones fell silent, then simply fell.

Kelvin would really appreciate the irony: that this defeat of the greatest representatives of current machine intelligence was wrought through the same two-and-a-half century old family of protocols for solving consensus, the Paxos algorithm, used at the birth of distributed computing, and which was, itself, the inspirational root source of PaxoSynchrony3’s name.

And still, the Tekhenu Tower fell. The final portion of the obelisk hurtled toward the ground, like the tip of a whip, gaining speed.

I didn’t see it land. I smashed down atop the furthest ReVo, obliterating its camera and lighting mount as the helodrone and I caromed off in opposite directions. I landed hard and spun to a stop, and found myself looking up at the design hub bridge. I was laying on my back only a few meters from where I had lost my previous lower half in the pathway, what seemed now a lifetime ago. A quick syscheck showed that other than a displaced elbow joint, I was tip top. I heard a familiar voice call out, in German.

I ran back into the quad. DT12 was lost. Teams of emergency bots rushed around trying to collect the precious contents of Tekhenu Tower. I found Kelvin under a giant shard of red granite that had blown off the obelisk, his lower half wedged between it and the tread of the lead ReVo. I rushed to free him, but he grabbed me by the hands to stop me.

“Spukhafte Fernwirkungen,” Kelvin said, quietly. “It lives.”

His face was beaming with joy. Another incongruity. And yet, as my builds continued knitting themselves together, I saw glimpses, the outlines of what Kelvin had been working toward, in lurches and starts, for the entire length of my existence. It was his holy grail. And it had to do with what Einstein, nearly three centuries earlier, had called Spukhafte Fernwirkungen, literally “spooky action at a distance,” referring to the concept of quantum entanglement. What it had to do with this, I didn’t comprehend. But I could see that Kelvin did.

“Rybos, there is hope for you yet.”

He smiled, and nodded, and closed his eyes. I noticed that I was kneeling in a pool of viscous fluids. A slowly widening slick of coolant, mixed with something else. Blood. Kelvin’s blood.