sticking carb heat control

The carb heat control cable is inside a metal outside such as the throttle and mixture cable.
Maybe there is a kink or to tight of a bend on the cable.
The cable attaches to the air intake box on the left side and attaches to a small lever that cycles a flap inside the intake box cycling fresh air and heated air for carb heat.
If you cant find any kinks in the wire you might try disconnecting the wire from the level on the air box and see when you move the lever whether or not the flapper is rubbing on something inside the air box assembly.
If the carb heat flapper moves easily and there are no kinks in the cable you might try applying some grease/lubricant inside the wire sheathing.

on my 415G, the carb heat control is similar to a lawnmower throttle cable, you can try lubing it by putting mouse milk oil on the outside and letting it seep into the housing, or you can try a motorcycle cable lube tool,
www.amazon.com/GTSpeed-Universal-Motorcy...%2Caps%2C1410&sr=8-4

415E C85 engine; my carb heat control has become hard to pull open and/or close. What is most likely cause? I am new to the coupe. Is the carb cable in a "sheath" similar to a Bonanza or is the cable just exposed without a covering? Is is attached to the left side of the carb (from cockpit) or the right? Thanks