Drum spins while agitating

Kenmore washer has started wrapping items very tightly around agitator by the end of a wash cycle. When observing the cycle, it appears that the drum spins in one direction and agitator cannot move properly as it should. If water level is high, the water will spray out over the sides of the drum during the “whirlpool” action that is going on, instead of proper agitation. Have checked the agitator dogs, and all seems fine with agitator. Can anyone suggest other things I could consider in troubleshooting this machine?

It sounds as if the washer actuator (shifter) is not locking in to agitation mode. This puts the brake on the drum to prevent it from spinning during agitation.
It may be the splutch assembly is bad not allowing the brake to engage.
Finally the transmission may be bad, not locking the brake.