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Preamble:- Turnouts from different manufacturers are a real mixture of electrical connection. Very often it is not possible to tell exactly what rail connects to what without measuring continuity with a multi-meter. I have gone through my various designs and catalogued them and the possible uses they might have.

Here are the names of the point rails and
the various terms used to describe them.

All Powered - both exit tracks are powered
Power Switching - only the exit track powered
Solid frog - all rails in the frog area are common electrically
Split frog - separated electrically - not common
DCC Safe - blades and stock rails electrically linked

Point component names
Some points to note in the diagrams -

Stock rail, Closure and hinge are jumpered.

All rails must be common - note rail at frog point.
If frog was split there would be a wheel short on the frog point.
The Atlas code 55 "N" scale point is an 'All Powered" type. That is, the track power from the toe connection is present on all exit rails. Most useful in a main line situation.
The frog is a solid metal casting with its own connection. Each through rail is jumpered to the one past the frog.
The blade and closure rails are bonded to the adjacent stock rails.		 Atlas all powered turnout
Pro: Blade and stock same potential, Mostly used as a main line point, Insulated joiners not needed. Con: Not best as a loop or yard point, Needs frog powered from a switch or run as an unpowered frog.
Bachmann "N" scale all live with insulated frog. The blade hinge pivots are loose and don't make good electrical contact with the closure rails.
There is a plastic insert for the frog and wing rails and the closures are jumpered to the rails past the frog. It is "All live" construction.		 Bachmann N scale - all live
Pro: DCC safe construction but needs hinge bypass wire. Insulated joiners not needed Con: Insulated frog can cause power loss to loco's, Poor construction at hinge,
The Peco HO point was an early insulated frog type. The frog wing rails were metal and unconnected to any other rails. The frog point was a plastic material.
Each closure rail is jumpered to the rail past the frog. Electrical contact to the blade is helped by an over center spring on the throw bar. The unused blade has no electical contact so the rail past the frog is not powered on one side and protected the turnout from incorrect entry. 		Early Peco turnout
Pro: Sprung tie bar for good blade contact, Reverse entry protection. Con: Unpowered frog area may cause power loss.
The Peco Insulfrog point in "N" scale has a plastic frog and wing rails.
Each closure rail is jumpered to the rail past the frog. The unused blade has no electical contact so the rail past the frog is not powered and protected the turnout from incorrect entry.
An over center spring at the throw bar makes a positive electrical contact between the blade and the stock rail.
Peco N scale insulfrog
Pro: Sprung tie bar for good blade contact, Reverse entry protection. Con: Unpowered frog area may cause power loss. Insulated joiners needed if a loop entry.
The Peco Electro-frog point in "N" scale is all metal with plastic guard rails. The plastic base in the frog area can lift the wheel rims on older wheel sets and cause contact loss and bouncing.
The unused blade has no electical contact so the rail past the frog is un-powered. Some examples have been seen with the frog wired to both closure rails (dotted line) so insulated joiners would be needed.		 Peco N scale old
Pro: Power switching, Sprung tie bar for good blade contact. Use on main line. Con: Insulated joiners are needed as offset frog point rails can make wheel contact and short.
The Peco Electro-frog point in "N" fine-scale is all metal with plastic guard rails.
All frog rails are wired together so the unselected rails have the frog rail polarity. Normally, insulated joiners are used on them to avoid shorts. An over center spring at the throw bar makes a positive electrical contact.		 Peco N fine-scale
Pro: Power switching, Sprung tie bar for good blade contact Con: Insulated joiners are needed past frog rails.
Not a main line point.
Peco Finescale converted to DCC safe. The Frog rails are isolated by cutting the main rails. A flexible wire is soldered round the hinge and across to the stock rails, some of the sleeper plastic can be cut away underneath.
The original frog jumpers connect all rails together and the power to them must be supplied by a point actuated switch as normal.		 Converted to DCC safe
Pro: All electrical contact points are solid. Blade and stock rails are at common power levels. Con: Need switched power to the frog rails.
Shinohara "N" scale basic turnout. All frog, closure and blade rails are joined. Power is supplied through the blade to stock contact, but would be better if supplied by a point actuated switch to the frog.
It has a metal guard rail. All track on the unselected side is at the stock rail potential.
This is the usual setup for hand-made turnouts.		 Shinohara basic turnout
Pro: Con: Must be isolated from track past the frog, unless going into a yard backshunt.

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Preamble:-Drivers for the point motors will depend on the motor construction and the turnout type. If a turnout has an over center throw bar spring this keeps Blade and Stock rail contact positive. The motor power can then be removed after throwing the points. However if there is no positive contact the motor must keep up a pressure on the blades. This will determine which type of motor is used.

Twin Coil or Twin Solenoid motors need a high impulse current pulse for a short time. Any longer than 1/2 a second and the coil will overheat as it has a very low resistance. In the CDU the capacitor holds a charge which passes a high current initially untilit discharges. The capacitor cannot recharge until the push switch is released. It will recharge in about 1 second. Capacitor Discharge Unit
An alternative circuit.
The push button switch on the CDU must be robust as it has to pass a high initial current. If a lighter switch or relay is to be used then this circuit is ideal. The switch can be center off or a standard toggle switch. When it is switched it causes a positive pulse to activate the transistor and drive a current pulse through the coil. The pulse length depends on the 4u7 capacitor which may be changed in value if needed.
Single Coil motors are un-common. They use a magnet to bias the coil and reverse the drive current to change the position.
Here is a Hobby Motor adaption that I used for "N" scale turnouts. The motor is a 3 volt 3 pole cheap hobby motor. Its movement is limited to about 1/3 of a turn and it throws a lever that moves the throw bar. Only about 2mm movement is needed for this scale. An over-center spring is used to hold the thrown position (Atlas points). The 3D picture shows the linkages.
motor-right eye motor-left eye simple capacitor discharge
The Low Current motorised (stall motor) needs a constant power to the motor to hold the blade positively against the stock rail. The commonest of these is the Circuitron 'Tortoise" motor which also has 2 change-over contacts for frog power or signalling etc. Control is simple. Either a 12 volt DC supply and a double pole change-over switch or an A.C supply with 2 diodes and a single pole change-over switch can be used. A number of additions are possible to the basic circuit.
The enclosed change-over contacts are low current and if used to supply the frog can be cooked by a prolonged track short circuit. A supplimentary relay for more power handling can be added. A dual LED could provide a trackside 2 aspect signal. Indicator lamps can be mounted on the control panel, as shown.
Connections to the motor can be soldered (most common) or made by a PCB Edge Connector plug. There is one available commercially with double sided connections.		 Tortoise motor options
Motor driven type use a worm drive to move the points more slowly.
They have limit switches so that power is removed when fully thrown. A worm drive has no backlash and will lock the throwbar.
Power from a DC supply is supplied via a reversing switch . Some makes have change-over switches also for Frog or Signal control.
I have used a Radio Control Servo to actuate the turnout. They are rotary (about 180 deg) or with a linear output arm. They can be controlled very preciesely, electronically. The electronics needed is more complex and a five volt DC supply is needed for the servo motor. See Servo Motor Control for circuit details.

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Links to Tortoise Motor information.

To Amhobby description page for Circuitron products.
Tortoise™ Manual PDF Adobe Reader file about - 200Kb
Plus Tortoise™ Application Notes, on site, explaining mounting, wiring, possible problems.

TORTOISE SWITCH MACHINES AND CONNECTORS - Tortoise slow motion switch machines. Edge Connector for easy installation. ... :. Edge Connector (5 pack) ... Greenway Products

Wiring for DCC by Allan Gartner The Tortoise is a slow-motion switch machine after all and it takes some time to flip the points. If you change the frog voltage source before the points have flipped then you may make a momentary short circuit.