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[Reply #15 on:]

*If* the strain gauges are of the sort where one element increases its resistance and the other decreases, then to use all 4 I would connect them like this. Let the 3 terminals of each one be called C (common), I (increase) and D (decrease). Connect them in a ring using the I pins and D pins so that each I pin is connected to another I pin and each D pin is connected to another D pin. Then use the four C pins as the bridge inputs and outputs.

What this gives you is a bridge in which one of the resistors is made up of two I elements in series, its two neigbours are each made up of two D elements in series, and the diagonally opposite resistor is also made up of two I elements in series.