The antonyms for the word "jerked up and down" would be smooth, steady, and constant. When we think of something that jerks up and down, we imagine a rough, uneven movement. Conversely, smooth would indicate a fluid motion, lacking any sudden jolts or interruptions. Steady would imply a continuous, uninterrupted flow, whereas constant would suggest a regularity of movement, perhaps at a certain speed or rhythm. Whether we're describing a machine or a person's actions, these antonyms are all useful for describing motion that is fluent, fluid and uninterrupted.