My motorcycle moving automatically to left side and jerk problem in handle bars what is the cause??

Counter steering the action that steers any two wheeled vehicle.
The art of counter steering is not thought about it happened automatically.
If you want to turn or swerve quickly push with your palm on the bars the direction you want to go.
So it you want to serve to the left quickly push the left handle bar with a quick push.
And Visa versa if you want to go to the right push on the right hand handle bar.

Check the clutch adjustment it may be not disengaging properly & you may need to wind out the outer cable on the handle bar left side

This is most likely caused by a loose connection behind the start button module on the handle bars. There should be 2 screws on the back of this module. Remove said screws and it should split apart in two pieces. You can then inspect the wiring to see if there is a loose connection.

Lift the bike off the ground (front end), turn steering side to side, should be smooth all the way (not notchy), check your tyres both front and rear, uneven wear, warped rim, should spin freely and true (wheel bearings) than check for fluids on your fork legs, your front fork seals may be leaking or the oil may be due for a change!!

Sit on the bike and turn the handle bars to the right. Look on the left hand side where the left handle bar was and you will see a rubber cap. Remove the left plastic cover panel around it and remove the rubber cap. It has hash marks to measure by. Ad 50/50 antifreeze till you see it half way up the hash marks. Be sure the rubber cap snaps back on tightly all the way around.If you ever need access to the radiator cap it is on the right side under that plactic cover. But you can add coolant on the left side. This is the upper level resivoir.

Hi Art! First of all, congratulations on your 1967 Triumph... that's a beauty!!!

Basic things to know before riding a bike is it's parts.

Clutch is the lever you press on the left side of the handle bar.

Front disc brake is the lever on the right side of the handle bar.

Shifter is the one you're stepping on when shifting gears and is located on the left side of the engine if you're on it.

Now, you must first know if the gear is on Neutral by pushing the bike before starting the bike. If it's hard to push then the shifter is not in neutral. Press the shifter by your left foot until you are able to push the bike with ease.

Hop on the bike and start the engine. Most bikes have ignition starters but if your bike doesn't have one, then you have to turn keys to on position and use the kick starter. Rev the engine by pressing the throttle grip on the right side of the handle bar.

Engine is running and in idle position. Press the Clutch lever (left hand) and press the shifter once (left foot) DO NOT RELEASE THE CLUTCH YET!!!

Slowly press the throttle with your right hand until you hear or feel the engine purr...

Slowly release the clutch (left hand) until you fell the bike move forward.

If I am not mistaken, shifting the gears of the triumph is 1-down and 4 up...

Every time you shift gears, you need to press the clutch to release the gears.

Hope you'll have fun!!!

Ride safe my friend!!!

Don't forget your riding gears!!!

^_^

Turn to the side and then engage the lock with the key.(you may need to push key in before it will lock)move it a little to the left or right to let the lock fit into the handle bar lug.

remove the controls and insulate the exposed wire from contact with the handle bar.

Sounds a lot like cable stretch. Have a local bike shop replace all the cables and do a derailleur adjustment. Costs is usually under $40 complete.