This $15 handlebar mount heroically holds an iPhone to my buzzing old BMW airhead's bars. Finding a mount that does was not a cheap, easy or fun experiment.
If you are going to clip your cellphone onto your handlebars and roll around at high speed you don't want the phone to break lose and go flying away. It can take a lot of time to find an old iPhone 4 on the side of the highway. I speak from experience.
After a few other mounts failed me, the safety strap on this High Grade unit caught my eye. It has both compression legs to hold almost any size phone in place and an elastic band that stretches over it, holding the phone to the unit. The band could get in the way of operating the phone, but my heavy leather gloves already do that. I simply turn the GPS on and leave it alone.
The mount installs easily. It should also work on bicycles with smaller diameter handlebars. The BMW I installed this on has the slightly smaller than ⅞" low EU bars, more standard 1" bars may have a more difficult fit.
