Precision Pendulum Assembly: Apparatus description
The pendulum apparatus is composed of three components: the supporting structure for the pendulum fulcrum, the launcher of the pendulum mass and the controller electronics.
The basic support can be a wall or a robust metallic structure like the one presented here. The choice for the bob was a training steel weight from the official shot put with 2kg. This weight has the advantage of having a drilled hole for holding an M4 screw and can be found in any good sports shop. This screw can be made of a threaded brass rod with 10mm length. A small 1mm hole is drilled on the rod were the pendulum cable is fixed using current soldering thin-plumb(or any silver-thin alloy) or by tying a proper knot. The cable used is from 0.4mm remanium wire that can be bought in any dentistry retailer.
The following drawings document the construction of the metallic pendulum's sections.
The support for the fulcrum is made from any robust and hard flat surface as for instance a brass or stainless steel piece with a 12-16mm hole. This surface has an indentation made with a diamond or hard steel blade which holds the pivot in place. With this design, slippage is avoided.
The fulcrum itself is made as well of stainless steel or brass consisting in a triangular prism with 50mmx9mm with a central 1mm hole in one face crossing the opposite edge. In this hole is soldered or glued an intravenous needle where the pendulum cable goes through and is secured by a small screw on the top.
Pendulum length limits
The launcher of the pendulum and controller electronics have limits which restrict the pendulum length and/or operation of the Precision Pendulum Assembly. Each one of those limits (min. and max.) are explained in the following subsections below. The last subsection (Limits) presents a table with the limits for the standard launcher and controller electronics used in the World Pendulum Alliance (WPA) apparatus assemblies.
The minimum length of the pendulum is mainly limited by the launcher speed. For a given launching distance, the shorter the pendulum the higher is the horizontal pendulum velocity. Therefore, the shovel acceleration should be high enough to make a clean release of the ball and the shovel speed should be high enough to make sure the ball never touches the shovel after it has been released. The shovel maximum speed and acceleration set the limits for the minimum pendulum length and they depend on the step-motor power voltage. The higher the voltage the higher the speed and acceleration the shovel can have. An additional constrain that may also be observed in too short pendulums is the risk of the ball going over the shovel for large launching distances.
There are two options that can be adopted to reduce the minimum length limit of a pendulum:
- Increase the setp-motor power voltage: In the standard/default WPA launcher configuration, the power voltage is set to 12 V. Some the provided power supplies can go up to 20 V. Increasing the power voltage too much may result in overheating of the motor. Care should be taken when performing this operation. A suggestion is to increase the voltage step by step while performing some experiments in between steps to verify that the motor does not overheat. A voltage up to 20 V should be safe to use.
- Limit the maximum horizontal launching distance: This options restricts the operational space of the launcher. By reducing the horizontal launching distance (initial angle), the maximum horizontal velocity and acceleration are reduced. The launching distance should be reduced to a point where the shovel can cope with the launching requirements (velocity and acceleration) without the risk of stalling half way during the launching process.
NOTE: In any circumstance, the initial angle should never exceed 45 degrees because the controller has not been programmed to deal with launching angles larger than 45 degrees.
The maximum length of the pendulum is limited by the controller electronics and it is associated with oscillation period. The longer the pendulum length the longer is the oscillation period. There are two limitations in controller:
- Watchdog timer: This timer has been configured by default to last about 16 s. As a result, it restricts the oscillation period of the pendulum to a value lower than 16 s. Higher values up to ~131 s can be configured for the watchdog timer.
- Oscillation period counter: This counter consists of a 32 bit counter (2 x 16 bit registers) and each count corresponds to 1/3686400 s (~271 ns, timer prescaler 1:1). This timer configuration results in a total maximum time of ~1165 s. Higher counter total maximum times can be obtained by increasing the timer prescaler (up to 1:256). In this case the timer resolution is decreased in accordance to the prescaler value.
Between the two, the main limitation is, by far, due to the watchdog timer.
A photo of the launcher used in the WPA is shown in the figure below. This launcher uses a V-slot rail technology and it is characterized by a maximum horizontal launching distance of 250 mm. The following table shows the pendulum length limits for this specific launcher.