A bad axle or CV Joint can cause vibration of the vehicle but usually not when braking.
if your vehicle is front wheel drive then it will have a CV joint and if your vehicle is rear wheel drive it will have a drive shaft and U Joints.
Bad U Joints or a bent or out of balance drive shaft can lead to vibration when driving down the road but the vibration should not occur when braking.
Usually vibration when braking is caused by stuck brake calipers, warped brake rotors, or the brakes grabbing.
A bald tire can cause a vehicle to shake when going down the road.
If the bald tire is out of round or the steel is starting to show through the tire then it can cause shaking of the vehicle as it won't be balanced.
Also make sure your tires and wheels are balanced as when wheels and tires are not balanced they can cause shaking of the vehicle and shaking of the steering wheel if the wheels are on the front of the vehicle.
Other causes of a car shaking or bad motor mounts, misaligned wheels, stuck brake calipers etc.
Cars or other vehicles shake because of an out of balance or defective tire, a bent wheel or a worn drive line U-joint.
Or even warped brake rotors, warped brake drums and even a bad axle either on the front or rear of the vehicle can cause a vehicle to shake.