Also utilized for a model of Chevrolet Corvair.

Since your question spurred my curiosity, I discovered the
informational DICTIONARY OF AUTOMOTIVE TERMS at
http://www.motorera.com/dictionary/car-dic.htm

The following don't precisely answer your question as far as the
origin of the word or usage, but, they are interesting nonetheless.

Spyder:
In the early 1900s, a light two-seater car. In the 1950s the word was
revived by some Italian manufacturers for an open two seater sports
car. Also spelled "spider."

Which led to:

spider:
   [1] On a bicycle, the multi-armed piece to which the chainwheels
are bolted, usually welded to or part of the right crankarm.
   [2] A four arm piece on a constant velocity joint.
   [3] A central crosspiece linking the two yokes of a universal
joint.
   [4] A cross-shaped wheel wrench with a different-sized box socket
head on each of the four legs.
   [5] A wheel spider
   [6] A type of sport vehicle. In the early 1900s it meant a light
two-seater car. In the 1950s the word was revived by some Italian
manufacturers for an open two seater sports car. Also spelled
"spyder."

Related image for  [2]:
http://www.100megsfree4.com/dictionary/c/constant.gif

And -
spider gear:
   A small gear (usually in a set of two to four gears) mounted on a
shaft pinned to the differential case. They mesh with the bevel gear
on the ends of the axles and drive them. Also see pinion gear.

And -
planet spider:
   A common type of planet carrier with a spider or web-style design

And -
wheel spider:
   A part of a cast/forged wheel which connects the rim and the wheel
hub and incorporates a spoke design