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

]]>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

]]>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

]]>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

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.

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

]]>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.

]]>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.

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

where a_{k} , b_{k} , c_{k} and d_{k} are real coefficients and theta ranges from 0 to .

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 a_{k} , b_{k}, c_{k} and d_{k} to define the link dimensions,

and the 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,

This equation identifies the curve as the end of a serial chain consisting of a sequence of links L_{1}, M_{1}, L_{2}, M_{2} and so on, such that the L_{k} links rotate counter clockwise and the M_{k} links rotate clockwise both at the rate .

The initial angles define the configuration of the serial chain when .

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

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

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.

]]>The 2016 Mechanisms and Robotics conference is part of International Design Engineering Technical Conferences organized by ASME International in Charlotte, North Caroline, August 22-24.

Plenary speaker Bernard Roth is the Academic Director of Stanford University’s d.school and the author of the Achievement Habit.

** For some reason, ASME has broken these links to the 2016 IDETC conference**, but you can find out more about each of the symposia at the conference overview link: 2016 ASME Mechanism and Robotics Conference Overview. Then select the Expand all Symposia Link to see the sessions and a list of papers.

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The input task is a planar motion given as a set of discrete positions and orientations and the app computes type and dimensions of synthesized planar four-bar linkages, where their coupler interpolates through the given poses either exactly or approximately while minimizing an algebraic fitting error. The algorithm implemented in the app extracts the geometric constraints (circular, fixed-line or line-tangent-to-a-circle) implicit in a given motion and matches them with corresponding mechanical dyad types enumerated earlier. In the process, the dimensions of the dyads are also computed. By picking two dyads at a time, a planar four-bar linkage is formed. Due to the degree of polynomial system created in the solution, up to a total of six four-bar linkages can be computed for a given motion.

MotionGen also lets users simulate planar four-bar linkages by assembling the constraints of planar dyads on a blank- or image-overlaid screen. This constraint-based simulation approach mirrors the synthesis approach and allows users to input simple geometric features (circles and lines) for assembly and animation. As an example of the Simulation capabilities of the app, Figure shows a walking robot driven by two sets of planar four-bar linkages where the foot approximately traces a trajectory of walking motion. The users can input two dyads on top of an imported image of a robot or machine to verify the motion and make interactive changes to the trajectories.

Anurag Purwar describes MotionGen and its applications in this video:

MotionGen is available as a free download at both Google Play- and Apple’s iTunes-Stores.

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