Our cabinet only has 24 VDC. The machine is rated 9–36 VDC — can we wire it directly, or do we need a separate power supply?

You can wire it directly; 24 V sits in the middle of the range. But check four things first. 1. Inrush current. At switch-on the machine draws a peak several times its running current for tens of milliseconds. If the cabinet 24 V supply is already near full load, that dip can trip its protection. Leave about 30% headroom, or give the computer its own supply. 2. Voltage drop. Thin, long cable means lower voltage at the machine than at the supply; a 9–36 V unit rarely reaches its limit, but measuring at the terminals under full load is still worth doing. 3. Protection. Fit a correctly rated DC fuse or breaker on the computer branch, and check whether the machine has reverse-polarity protection — many industrial models do, but reversing polarity on one that does not destroys it immediately. 4. Noise and surges. If the supply is shared with solenoids, contactors or drives, add filtering or give the computer a separate branch. If the cabinet loses power frequently, budget for a DIN-rail 24 V UPS as well.