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Notes
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Luminch One
Yes, you can use two 10ohm 1W or 1/2W in series, or also you can use four 68 ohms 1/4W in parallel.
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Luminch One
The LED in this lamp is rated to maintain 70% of its brightness after 50.000 hours. I had not checked the datasheets of all the components, but I suppose the LED is the one that wears faster of all them.
Anyway, as you have all the plans on how it is built, if some part fails just replace that part and it will remain alive.
Most probable cause of end-of-life will be that you get bored of it or want to use the Arduino for another project, that is why I included the end-of-life disassembly step.
I think we already have enough garbage on the planet and that is very important when designing new objects to think about how its parts can be reused at end-of-life and what impact on the environment will have throwing the non-reusable parts. For more info about EOL design search for Design for Disassembly.
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Luminch One
For all of you who want to design your own customized lampshade for the project, checkout the Pop-Up Card Designer software that I used to design the Luminch One lampshade.
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Luminch One
You can use octopart to search or also you can replace it with any NPN transistor that can handle a current of 500ma, just check the pinout of the replacement in its datasheet as not all the transistor have the pins in the same order.

Luminch One
1) You need to take in account the gain of the transistor you are using and the current you want to switch with it. If you have a high gain version of the BC337 like the BC337-40 you can use a higher value resistor and it will work OK.
2) The 100uF capacitors are for stabilizing the power source because the PWM of the LED introduces noise in the 5VDC and the distance sensor do the same because it consumes big pulses of current for driving its internal IR LED. I have not calculated it, I just tried with some capacitors I had around :)
3) I used a 18ohm resistor to limit the current to what I think the LED can withstand without and extra heat sink. If you add a heat sink you can use a smaller resistor to the send more current to the LED, but never more than 500ma that is the current limit for the BC337 and also for the Arduino 5V I think.