Hello, Geoff. I think that you will find that top and bottom dead centres (points of maximum swing of the beam) occur when a straight line is drawn through the centre points of the crank pin, the crankshaft and the con-rod / little end; i.e. when the centre line of the con-rod aligns with the crank pin centre line.

When the crank pin is 'up', it will be a little closer to the cylinder than the true vertical centre line and when 'down' will be slightly further away from the cylinder.

The angular displacement of the crankpin from the vertical cenre-line of the crankshaft will not be the same for TDC and BDC, but the difference is very small and of no account for all practical purposes.

Geoff G

Not necessarily, it depends on the exact horizontal distance between crank axis and beam pivot. If this distance equals the half beam length then Geoff is correct, but if slightly reduced so that crank is directly below the little end pin at both centres, then symmetry rules. Pedantic people like me allow for that sort of thing, very probably a waste of time!

You'll have even more fun when you come to figuring out the Watts parallel motion linkage at the other end of the beam. Enjoy!

It is taken as read that the Piston Rod is vertically below the pin at the cylinder end of the beam, at Inner and Outer dead centre, using the Watts linkage to cope with the "vibration" .(because of the arc ) at intermediate points

In the same way, that the Crankshaft axis is vertically below the pin at the other end of the beam.

The beam does not have to be equal about the pivot point. Although many were pumping engines, it was quite usual for Cornish beam engines to have asymmetric beams.

Howard..