## Design Research in China: Xi’an

Design Research Xian

This video of our visit to Xi’an captures the beauty of the city and its surroundings, as well as the personality of the excellent professors and students at Xidian University.

For our colleagues in China, here is a link to a Youku version of this video: http://v.youku.com/v_show/id_XMTg2MzQ5NDI4MA==.html

Youku Xian Video

## Prototype of the Trifolium Mechanism

Trifolium prototype

Yang Liu and Peter Yang designed and built this physical prototype of our Trifolium mechanism.  It is fabricated from ABS using the Stratasys Fortus system in UCI’s Institute for Design and Manufacturing Innovation.

Our Chinese colleagues can view this video on Youku at the link: http://v.youku.com/v_show/id_XMTg2MzQ2MjE5Mg==.html

Youku Trifolium Prototype

## 2016 UCI Energy Invitational Video

2016 Energy Invitational

Here at UCI we are hard at work on three different race cars for 2017 competitions. It is a tough time, as it seems things move too slowly. I offer this video of highlights from the May 21, 2016 UCI Energy Invitational on UCI’s campus to inspire all of our race teams as they work to prepare their cars for the 2017 Energy Invitational. Many thanks to Vital Link and UCI Anteater Racing for their support of a terrific event.

For our colleagues in China, here is a youku.com version: http://v.youku.com/v_show/id_XMTg0MzI5ODY3Mg==.html

2016 UCI Energy Invitational

## Design Research in China: Tianjin

Design Research Tianjin

Chris McCarthy filmed and edited this video of our visit to Tianjin, which showcases the design research in mechanisms and robotics at Tianjin University and captures the energy and beauty of the city and its people.

For our colleagues in China this video is available on youku.com: http://v.youku.com/v_show/id_XMTgzMTIyMTg1Ng==.html

Youku Design Tianjin

## Manufacturing Prototype for the Butterfly Linkage

This animation is taken from Yang Liu’s detailed design drawings for the manufacturing prototype of the Butterfly Linkage. The component parts are to be constructed by additive manufacturing.

This animation includes the music of Explosions in the Sky:

For our colleagues in China this animation is available through youku.com: http://v.youku.com/v_show/id_XMTgzMzA5ODQyOA==.html

Youku Prototype Butterfly

Recent research on the design of linkages by Yang Liu has resulted in “Bezier linkages” that can be used to draw arbitrary Bezier curves. The trick is to use trigonometric Bezier curves. This whale consists of four Bezier segments and is drawn by four Bezier linkage elements.

This youtube version includes music by Explosions in the Sky:

A youku.com version for colleagues in China can be seen here:
http://v.youku.com/v_show/id_XMTgzMjU4NTQwMA==.html

Whale on Youku

## Three seconds

Three seconds

This second collaboration between Prince EA and Change for Balance won 1st Place at the Film4Climate competition.  The winners were announced at the United Nations Climate Conference (COP22).  This Film 4 Climate Global Video Competition is organized by Connect 4 Climate.

## Love and Bananas

Love and bananas

Beautiful scenes of Cambodia and Thailand and a road trip with an Asian elephant in this featurette make this a much anticipated documentary.

## Robot Ethics

Springer Handbook of Robotics

I found this excerpt of the TEDx talk by Bruno Siciliano describing the growing research area of Roboethics to be fascinating and important. Prof. Siciliano is the Director of the ICAROS Center at the Universita degli Studi di Napoli Federico II. He is co-editor with Oussama Khatib of the first and second editions of the Springer Handbook of Robotics. The entire talk is available at the link Robotics and Napoli.

## Design of Drawing Mechanisms

Mechanical systems that draw trigonometric curves provide a versatile way to draw complex curves. Yang Liu designed this serial chain consisting of 14 links coupled by a belt drive to draw the Butterfly curve.

The Butterfly curve is an example of a trigonometric plane curve, and our study of Kempe’s design of linkages to draw algebraic curves has lead us to a way to design serial chains that draw these curves.

Here is how it is done.

Butterfly curve

Trigonometric curves. A trigonometric plane curve is a parametrized curve with coordinate functions, P = (x, y), that are finite Fourier series,

Trigonmetric equation

where ak , bk , ck and dk are real coefficients and theta ranges from 0 to $2\pi$.

A large number of well-known curves have this form, such as Limacon of Pascal, the Cardioid, Trifolium, Hypocycloid and Lissajous figures.

A coupled serial chain. Without going into too much detail, it is possible to use the coefficients ak , bk, ck and dk to define the link dimensions,

and the initial angles,

Initial angles

These parameters allow us to redefine the trigonometric equations of the curve as the coordinate equations of the links of a serial chain,

Serial chain equations

This equation identifies the curve as the end of a serial chain consisting of a sequence of links L1, M1, L2, M2 and so on, such that the Lk links rotate counter clockwise and the Mk links rotate clockwise both at the rate $k\theta$.

The initial angles define the configuration of the serial chain when  $\theta=0$.

The Butterfly drawing mechanism. The trigonometric curve of the Butterfly linkage is defined by the coefficients in the following table,

Table of Butterfly coefficients

These coefficients are used to calculate the dimensions and initial configuration of the serial chain listed in the following table,

Table of Butterfly link dimensions

The result is a serial chain consisting of 14 links that are coordinated to move together as the base rotates. The end-point of the chain draws the Butterfly curve.

Butterfly drawing mechanism