On the older black cast Singer machines sometimes the motor can spin but there is no drive to move the needle bar. The most common cause of this problem is usually the washer located directly under the de-clutching hand screw which secures the machines handwheel. The hand screw can be removed by simply removing the single locking screw then unscrewed. The washer with two raised prongs will then be visible. This maybe worn and need replacing although it can be moved round one notch and relocated, also it's worth checking that the washer is fitted the correct way round with the raised prongs facing towards the machines top shaft and not away.
While the washer is removed it is good practise to remove the handwheel add a little oil to the top shaft and inner handwheel for smooth operation.