Pendulum Clocks A pendulum oscillates with a frequency of: g is gravitational acceleration R is the length of the pendulum (pivot to center of mass) Frequency does not depend on weight of the Bob g = 32 ft/s2 on earth R
How fast would a 1 ft pendulum swing? Freq. = 0.9 cycles/sec. = 9 cycles/10 sec. • = 3.14 g = 32 ft/s2 on earth
The torque of the gears keep the pendulum going. The gears get energy from the potential energy of the weight or spring in the clock. Winding the clock raises the weight or tightens the spring. The escapement ensures that the energy is released in small increments over a long period of time (e.g. daily or weekly). The pendulum length determines the frequency of the tick-tocks. http://electronics.howstuffworks.com/clock3.htm
http://en.wikipedia.org/wiki/Escapement When watching this animation, notice that the gear’s tooth gives a little push to the pendulum so that the pendulum continues to oscillates. The escape tooth slides across the pallet, exerting a small force on it. This small force exerted each cycle keeps the pendulum moving.
Anchor Pallet Escape Wheel Escape Tooth http://www.geocities.com/mvhw/anchor.html Energy is allowed to “escape” each time a tooth is released.
This is a clock with only a second hand: This axle is rotating (40/16)x(40/16)x(40/16)x(40/16)x(16/120) Or 5.2 times slower. Every 5.2 minutes the Weight wheel rotates once. The pendulum oscillates at two cycles/sec Period = ½ second. Second hand is directly connected to the Escapement gear
Effects of Temperature • Pendulums expand when heated causing R to get longer, making the clock slow down and lose time. • In colder temperatures lubricants become thicker increasing friction. Some clocks might stop if not enough energy is given to the pendulum with each tick.
From clock to watches (portable clocks) Replace pendulum with a small hair spring and balance that oscillates at a certain frequency if regularly energized. The hairspring coils and uncoils. The hairspring and balance are made to oscillate at a specific frequency. The hair spring is made from an alloy that can take the constant coiling and uncoiling. http://elginwatches.org/help/what_is_a_watch.html
Mainspring is the energy source. • Escpapement ensures that energy is released slowly and in constant increments. • Multiple gear trains control the hands. Hands line up in the center with slower moving hands mounted on hollow spindles. Watches are Energized with a main spring instead of weights.
Springs Springs store energy: F = k * x PE spring = ½ k * x2 k is spring constant (stiffness) x is the amount of displacement or how tight the spring is wound As the spring slowly is allowed to unwind, it does very small increments of Work on the clock.
Self Winding Watches An Oscillating Weight moves as the wearer’s wrist moves. The mainspring is automatically wound. http://www.timezone.com
Resources http://electronics.howstuffworks.com/clock.htm http://www.engineerguy.com/comm/3926.htm http://www.engineerguy.com/comm/4340.htm
Videos: • Da Vinci’s Clocks: http://www.youtube.com/watch?v=QMpd811EeyE http://www.youtube.com/watch?v=e-RR0H_4DYA
Assignment: • Reverse Engineer the Westclok Alarm Clock • Do not break the clock works or case. • Draw the mechanics that relate to the second, minute, and hours hands. Label the primary parts. • See lab handout
Plan vs. Elevation View of a clock works http://www.horologist.com/escapements.htm