The Spring-Balanced Desk Lamp
An adjustable desk lamp with springs instead of a counterweight stays balanced at any angle you set it to. This idea models the spring forces and lever arms that make that possible.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
A spring-balanced desk lamp (the classic 'anglepoise' design) uses a jointed arm with springs stretched between its segments, rather than a hanging counterweight, to hold any position you set it to without drifting up or down. As the arm's angle changes, the spring's stretch and its lever arm about each joint both change; for a well-designed lamp the two changes cancel so that the net turning effect from the springs matches the turning effect from gravity at every angle, not just one. This exploration analyses the geometry of the linkage and the physics of a stretched spring (Hooke's law) to find the spring stiffness and mounting points that keep the lamp balanced through its whole range of motion, and compares that with simpler counterbalancing systems such as garage doors or crane counterweights, where balance typically holds at only one configuration or must be actively adjusted.
Guiding Questions
- Measure or sketch the geometry of an adjustable lamp arm (or a simplified two-bar model). How does the angle at the base joint change as you tilt the lamp head?
- A stretched spring exerts a force proportional to its extension (Hooke's law). Express the spring's turning effect about the joint as a function of the arm's angle.
- Find the spring stiffness and attachment points that make the spring's turning effect match gravity's turning effect at every angle, not just one.
- Test your model: does a real desk lamp stay balanced through its whole range, or only near certain angles?
- Compare this always-balanced spring linkage with a simpler counterweight system, such as a garage door or crane counterweight, that only balances a single fixed load. What is the geometric difference between the two approaches?