There are a number of ways that come to mind. In the example of 10mm to 4mm, a simple one if both are stranded then a 10mm barrel crimp, with the 4mm folded to fill the side to the equivalent of 8mm. 

There are various large sizes of wago-like clamp, and for smaller transitions say 6mm to 2.6mm there are lever wagos

the larger sizes are intended to go in a box with a DIN rail profile to hold things still and need a screw driver to open the springs

10mm2 example

A few are made that will take meter tails  

If you are confident then soldering is always an option. When wires get chunky then rather than try and twist them and then solder, as you might up to about 1.5mm2, it is better to lay the pre-tinned cores side by side for a cm or 3,  and 'whip' them together with a length of much thinner tinned copper wire such as strands from some flex before soldering. However this approach is not for the faint of heart, especially with PVC insulation, as the balance between getting heat in fast enough that the joint is properly wetted and the solder fills the interstices, and over cooking it so the insulation burns back, is one that needs a few practice shots to perfect, and an iron tip size and power that matches the job,

Then as you mention there are resin filled joints,  and again the thin side will need to be packed, either by folding the wire, or sistering up with dummy strands.

There may be other better techniques that others will suggest.

Mike.

mapj1 said:

it is better to lay the pre-tinned cores side by side for a cm or 3

I was taught never to use pre-tinned for mains, as it makes a resistive joint, and tight copper-to-copper so the amount of solder flow between them is limited. Granted, far worse with lead/tin solder than silver/tin.

Maybe the solder resistance comes into it in some odd cases, but I'd hope that in a mechanically strong joint the lay-beside length is several times the cable diameter, so the solder cross section in the current path is at least an order of magnitude larger than  the copper cross section and probably more  - it is why high current solder joins are not made end to end - so not done like the fused ends of a broken bone, but instead side by side so more like a splint on a leg.

The electrical conductivity of lead tin solder and modern unleaded stuff  are both comparable, and actually similar to, or slightly more conductive than, many steel alloys, and about twice  as resistive as the same shape made in bronze, brass and the typical braze metal you may find in  terminals and fabricated bus and lightning conductor. (the brassy thermite weld  is also very similar.)

Solders and most electrical steel alloys come at about 0.12 to 0.15 micro-ohm meter (mechanical steels can be rather more) and the bronze and brass alloys being quite variable at around 40-70 nano-ohms meter, and pure copper at about five to 6 times more conductive than brass at  just 16 nano-ohms meter,

(i.e  copper is  ~ 16 milliohms for a 1mm2 core 1m long and the same wire made in brass would be 5 times that and if you had a solid solder wire - though do not be fooled as the stuff on the reel it is really  tubular flux filled stuff, resistance  would be perhaps ten times the same cross section made in copper, and more or less the same would be  true of  piano wire or typical steel strands on SWA armour. )

Mike

edited for typo and grammar.

I was taught never to use pre-tinned for mains, as it makes a resistive joint

Weren't most mains cables tinned during manufacture in the old imperial days? (originally to prevent sulphur in the vulcanised rubber insulation affecting the copper, but the practice seemed to continue into the days of PVC - certainly imperial T&E), Presumabbly if tinning were a problem it would be so for screw joints as well as soldered.

   - Andy.

BS7671:2018:Amd2:2022 Regulation: 526.2 Where a soldered connection is used the design shall take account of creep, mechanical stress and temperature rise under fault conditions.

Regulation 526.9.2 prohibits tinning of multi-wire, fine wire and very fine wire conductors if screw terminals are used.

Likewise 526.9.2 prohibits tinning of multi-wire, fine wire and very fine wire conductors if there’s relative movement between the soldered and non-soldered parts of the conductors.

When appliance manufacturers tin conductors of appliance flexes I normally cut them back and throw the tinned part away.

AJJewsbury said:

Presumabbly if tinning were a problem it would be so for screw joints as well as soldered.

There's a difference between someone with a soldering iron applying a thick layer of lead and tin via solder ('pre-tinning') vs a layer of higher-concentration tin (much lower concentration lead as it used to be) during manufacture of tinned copper conductor.

Tinned ends (with solder, particularly lead-tin solder, but also quite possibly silver-tin) are a problem for screw terminals ... Regulation 526.9.2 ... whereas the use of tinned copper wire is not.

Tinning a flexible stranded conductor into a solid mass makes it mechanically weak at the point the stiff bit meets the untinned part and prone to failure there. Of course if the wiring is loomed and only vibrates, rather than flexes, it is a perfectly sensible thing to do, and when done correctly fine for aircraft, space vehicles and a great many situations.It is not a suitable technique for the inexperienced, hence it being the last in my list. Soldered joints in that case must be stiffened by heatshrink sleeves or rubber, or similar so there is no flex on the strands at the solder neck. Using it as a poor substitute  for a ferrule without any such precaution is not usually wise.

Mike.

Graham, just to introduce a sense of perspective - how much resistance does an average in-service but aged light switch have across it's contacts? Or even a male to female contact resistance of a plug and socket outlet whose appliance hasn't been unplugged in a decades?

You can use a big choc block or a Henley block if room permits.

Z.