On some furniture the manufacturer used different kind of thread. One example are furniture from Fritz Hansen, their early production used inch screws, later metric.
Also Poul Kjaerholm furniture, made by E. Kold Christensen, used inch screws. Later in 1982, when Fritz Hansen has taken over the production, they changed it after some time to metric.
Also Vitra used inch screws on early Eames arm-and side-chairs. But if labeled as Herman Miller, it indicates not always inch thread, some of them are Vitra production and have metric thread.
Most of them have a relief-like “V” underneath the seat shell for Vitra project. They in most cases need metric screws.
If you are not sure if the screws used at your furniture you can take a screw you have, and compare the thread. Let me explain how:
E.g., if you live in an area where usual inch thread is used, take a screw same diameter you have in the garage, and put the teeth of the thread on the theeth of the screw from your furniture. If the thread fits exacly into the thread of the other, it is the same. In our example inch. So if you have an inch screw, and the thread of the screw of your furniture fits into the thread, you need to order inch screws.
If it do not fit, it is a different thread, The example below shows inch and metric.
It do not work in all cases, but in some!