The metal chassis is most definitely touchable, it forms the base where you fit the bowl, the bit that pivots up and holds the motor and the control knob. I would also include the gearbox as that's metal cased and bolts onto that second part, so potentially that might extend to the attachment as well since the connection to the gearbox is metal to metal.
OK - see below.
I'll need to look for the symbol. The mixer dates from 1982, did they have double insulated classification then?
Ours is a fair bit older than yours - early 70s, if not earlier, and does bear the Double-Insulated symbol - but I see that you've now found the symbol on yours.
The motor wiring, I must say I don't really understand why this would be "double" insulated but then I don't know how that term is defined. Note the exploded capacitors and cooked resistor by the way. ...... When fully assembled that wiring is covered by a plastic shroud, so when the mixer head is tilted up, those uninsulated leads and soldered connectors aren't finger touchable (is this shroud the "double"?)
"Double insulated" refers to the fact that there are two layers of insulation (OR one layer of 'reinforced insulation', whatever that may be!) between (electrically) live parts and any touchable metal.
Cheers. What would be the danger from adding one?
It is clear, in both yours and my (older) one, that the mixer is designed and manufactured to be Class II/Double-Insulated, and hence 'safe' without any earthing, that achieved by the double (or reinforced) insulation between live parts and any touchable metal - i.e. any 'touchable metal' is electrically 'floating', not in electrical continuity with anything else.
Given that, the only advantage of earthing the chassis would be to provide you with protection should there simultaneously be an electricidal fault within it and a failure of the 'double insulation' - an incredibly unlikely occurrence.
As for 'any danger' (of earthing the chassis) , it is again an extremely small 'risk' we are talking about. As a general truth, it is desirable that one should avoid having touchable metal which is 'unnecessarily earthed'. The reason for that is if one were to touch something else live (like a metal kettle that had become live due to a fault) and simultaneously touched the 'unnecessarily earthed' metal, then one would get an electric shock, whereas one would get little or no shock if the metal one touched was
not earthed (i.e. 'electrically floating'). However, as said, that is also an incredibly unlikely occurrence.
For what it's worth, I would personally trust the design and manufacture of the mixer and leave it unearthed.
Kind Regards, John