3) the tensioning spring on the tranny pulley is probably weak so when the harsh jerk happens the belt goes loose a bit so it then slips a bit.
4) the pivot point on the tensioning arm floggs out oval over time cause they never get lubed by home owners who do their own maintenance.
The tranny might be a little low in oil or need to have it replaced.
Down side is you usually have to pull it out in order to check it.
Normally I would make the effort to copy the images to my computer so they can be directly uploaded into the forum.
But as you decided not to do that making things difficult for me, why should I bother making things easier for you.
In the following image https://www.partstree.com/models/936038-960460002-00-ariens-42-lawn-tractor-19hp-kohler-hydro/drive-2/
You will see some pulleys , 50 & 52. there are the tensioning pulleys that may need replacing.
The plate 189 that they bolt into has a bush 186 that wears but no one ever bothers to check it.
It then allows bolt 185 to flog out the hole in the plate 189.
After that the link rod 279 flogs out the holes at either end of it cause no one ever bothers to lube them or the entire shifting mechanism , shaft 175 and all the bits that attach to it.
Then there is the brake rod . 79 .
Some where on it will be an adjusting nut to get a balance between braking and clutching as the one pedal does both.
For older people I back the brake off a bit so the mower is just rolling by the time the clutch takes up
It is prudent to test the parts , work out what is faulty and replace these parts.
Having said that Jerkiness can be caused by pulleys A & B.
Pulley C does little as it is on the slack side of the belt and is just there to stop the belt flapping around when the brake is applied.
I would be looking closely at the bush, the plate and everything that moves the plate.
Also have a good look at the brake adjustment
A brake that stays on too long after the slack in the belt is taken up will cause the mower to lurch violently
Two things I would also check. First is the condition of the belt, worn, cracked, or pieces missing will cause this problem. Second, does the tensioner arm which moves pulley B and possibly A must move very freely and smoothly.
Firstly that belt is toast judging by the crack in one of the photos.
Secondly it is either the wrong belt or is severely worn.
The proper belt , which is expensive is a wrapped kevlar fibre belt.
That belt appears to be a plain unwrapped el cheapo ( cause I know better than all those thieving rat bags who force me to buy those overpriced funny colour belts when a regular one at 1/4 the price will work fine ) belt.
If it is a plain unwrapped belt then you problem , or a large part of it, lies there.
Unwrapped belts are designed NOT TO SLIP .
They quickly get hot & sticky just like your car tyres.
Wrapped belts are designed to slip for the purpose of clutching.
Your belt should be # 21546076 which is an A 90.375" belt.
Plain belts are made in whole inch sizes only so pretty sure you will find it is a plain A90 belt.
If Mr Half Witt had bought a wrapped Kevlar A 90 he may have gotten away with it
But using a plain belt that is also 3/8" too short is asking for trouble.
Firstly that belt is toast judging by the crack in one of the photos.
Secondly it is either the wrong belt or is severely worn.
The proper belt , which is expensive is a wrapped kevlar fibre belt.
That belt appears to be a plain unwrapped el cheapo ( cause I know better than all those thieving rat bags who force me to buy those overpriced funny colour belts when a regular one at 1/4 the price will work fine ) belt.
If it is a plain unwrapped belt then you problem , or a large part of it, lies there.
Unwrapped belts are designed NOT TO SLIP .
They quickly get hot & sticky just like your car tyres.
Wrapped belts are designed to slip for the purpose of clutching.
Your belt should be # 21546076 which is an A 90.375" belt.
Plain belts are made in whole inch sizes only so pretty sure you will find it is a plain A90 belt.
If Mr Half Witt had bought a wrapped Kevlar A 90 he may have gotten away with it
But using a plain belt that is also 3/8" too short is asking for trouble.