Gear wheels Gear wheels Gear wheels
Gear wheels are often needed for drive transmission and for moving arms and grippers.
They are available as packeted kits of plastic gear wheels of a range of diameters from various manufacturers. Tamiya produce sets of gears, including motors, that can be assembled into gearboxes of many different ratios. Meccano and Lego produce gear wheels too, and the kinds of mechanism that can be built from them are shown in the photos overleaf.
Gear wheels transmit turning force by engaging their teeth. The number of teeth on the wheels matters more than their diameters. When talking about gear wheels we speak of
‘24t’ wheels and ‘36t’ wheels, meaning wheels with 24 and 36 teeth.
example, wheel A, with 10 teeth, is driven by a motor and engages with wheel B, which has 40 teeth. As A rotates one revolution its 10 teeth mesh with 10 teeth of wheel B. But B has 40 teeth, so has turned only a quarter of a revolution. Meshing a wheel with few teeth against one with more teeth gives a reduction in speed.
In the example, the gear ratio is given by the numbers of teeth on the two wheels. The ratio is 40 to 10, or 4 to 1, generally written as 4:1. An electric motor turns at high speed, generally at several thousand revolutions per minute. If a motor turns at, say,
16000 r.p.m. and drives wheel A, then wheel B will turn at a quarter of that speed, which is 4000 r.p.m. As an equation:
speed of B = speed of A ×
4000 r.p.m. is too fast for turning a robot’s road wheels. The speed would be less if A had fewer teeth and B had more, but there is a limit on how small we can make A and how large we can make B. Instead we put a third wheel C on the same shaft as B so that they turn together. C has few teeth, say 10. Wheel C is meshed with a fourth gear D, with more teeth, say 40.
The speed ratios are like this:
A to B 4 to 1
B to C 1 to 1 (on same shaft)
C to D 4 to 1
The overall ratio of A’s speed to D’s speed is 4 × 4 = 16 to 1. If the motor and A turn at 16000 r.p.m., D turns at 16000/16 = 1000 r.p.m.
This arrangement of gear wheels is called a gear train. The train described above needs a few more wheels to give a speed suitable for road wheels, but the principle of meshing few teeth with more teeth is the same. The simplest way to construct a train of gears is to build a gearbox from two panels of aluminium sheet or expanded PVC. The panels are bolted together, usually at their corners.
Some practical examples of ways of using gears and gear trains are shown on p. 42 teeth on A
teeth on B
The small wheel has ten teeth and the larger wheel has 57. The ratio is 5.7:1, so the larger wheel rotated at about one
sixth of the speed of the smaller one. Torque is increased about 6
times.
A worm gear. One rotation of the worm turns the the 58-toothed wheel by one tooth. The ratio is 57:1. Torque is high with
this type of gear. Note that this is a ‘one way’ gearing because it is not possible to rotate the worm by turning the large gear.
The large gear can be turnd only by rotating the worm. Shafts are at right
angles.
A crown and pinion gear is a reduction gear with the shafts at right angles. The smaller gear, the
pinion, has ten teeth. The crown has 50 teeth. The ratio is 1:5, so the smaller wheel turns five times faster
than the large wheel.
A reduction gear train reduces the speed of rotation and it increases the torque. This is the ‘turning force’, of the shaft. The amount of torque depends on the size of the applied force and its distance from the centre of rotation. Torque is measured by the sizes of the force and distance. For example, the torque of the motors used to drive the Quester (Project 6.4) is given as 2.1 kgf cm. It is the turning force produced by a force equivalent to 2.1 kg, acting on a wheel of 1 cm radius. A force of half that size (1.05 kgf) acting at double the distance (2 cm) has the same torque.
The torque produced by force f acting at a distance d is
T = fd
The motor turns the input shaft which has a pinion A meshing with a crown B. A small gear wheel C is moulded on to B so they turn as one. C engages with a larger wheel D, which has a pinion E moulded on it. D/E is a loose fit on the shaft. E meshes with a larger wheel F which has a pinion G moulded on it. G/H is loose. G meshes with a larger wheel
H and this is a tight fit on the output shaft.
The numbers of teeth are: A = 10, B = 36, C = 14, D = 36, E = 14, F = 36, G = 14, H = 36.
The A to B ratio is 1:3.6, the other three are ratios are all 36:14 or 2.57:1. The overall ratio is 1:(3.6 × 2.57 × 2.57 × 2.57) = 1:61.
For example, a robot gripper is holding a load of 0.2 kg and the arm of the gripper is 15 cm long. The arm rotates to lift the load. The torque required is 0.2 × 15 = 0.75 kgf cm.
A motor that develops a torque of only 0.5 kgf cm will simply stall when it tries to lift the load.
The secret of success is a reduction gear train, The Quester’s motors have built-in gearing with an 82:1 ratio. This reduces the rate of rotation of the output shaft to 1/82 times that of the motor, giving an output of 70 r.p.m. But, at the same time, it increases the torque to 82 times that of the motor (in practice, a little less because of friction).
The torque quoted for motors depends on operating voltage. The actual torque developed by a motor is less when it is run on a lower voltage.
Most applications of motors require some form of reduction gearing, but the same result can sometimes be obtained in other ways. A good example is the steering mechanism used in the robot toy (p. 249). The belt winds directly around the output shaft. The diameter of the pulley is 12.5 times that of the shaft, giving a reduction ratio of 1:12.5.