Sanding machine for processing a workpiece, comprising: - a housing; - a drive arranged in the housing for driving a drive shaft relative to the housing; - a first coupling part connected directly or indirectly to the drive shaft and provided with a toothing; - a first part which is provided with a second coupling part connectable in engaging manner to the first coupling part, and wherein the second coupling part is provided for this purpose with a toothing co-acting with the toothing of the first coupling part; characterized in that - the toothing of the first coupling part and the toothing of the second coupling part are mutually engageable crown gears; - the crown gears (8, 14) are clamped against each other and applied to transmit a rotating movement between parallel shafts; - the first part is a sanding foot; - the sanding machine further comprises first clamping means which are configured to clamp the crown gears (8, 14) of the first and the second coupling part (6,12) in engaging contact against each other and to thus form a self-centering clearance-free coupling; - the sanding foot is provided with a third coupling part with a toothing; - an attachment workpiece processing part is connectable in engaging manner to the sanding foot, and is provided for this purpose with a fourth coupling part with a toothing which co-acts with the toothing of the third coupling part; - the toothing of the third coupling part and the toothing of the fourth coupling part are mutually engageable crown gears; - second clamping means are configured to clamp the crown gears (20, 26) of the third and the fourth coupling part (18, 24) in engaging contact against each other; - the number of teeth of the toothing of the first coupling part connected directly and/or indirectly to the drive shaft and the number of teeth of the toothing of the third coupling part of the first workpiece processing part differ such that they have one or more common whole numbers as divisor and one or more common differing whole numbers as divisor; - the drive shaft is rotatable reciprocally through an angular displacement relative to the housing by the drive; and - the sanding machine comprises at least two exchangeable attachment workpiece processing parts in a first embodiment (22a-1) and in a second embodiment (22a-2), wherein the orientation in which the crown gear of the fourth coupling part is arranged on the attachment workpiece processing part in the first embodiment (22a-1) differs from the orientation in which the crown gear of the fourth coupling part is arranged on the attachment workpiece processing part in the second embodiment (22a-2). - a housing; - a drive arranged in the housing for driving a drive shaft relative to the housing; - a first coupling part connected directly or indirectly to the drive shaft and provided with a toothing; - a first part which is provided with a second coupling part connectable in engaging manner to the first coupling part, and wherein the second coupling part is provided for this purpose with a toothing co-acting with the toothing of the first coupling part; characterized in that - the toothing of the first coupling part and the toothing of the second coupling part are mutually engageable crown gears; - the crown gears (8, 14) are clamped against each other and applied to transmit a rotating movement between parallel shafts; - the first part is a sanding foot; - the sanding machine further comprises first clamping means which are configured to clamp the crown gears (8, 14) of the first and the second coupling part (6,12) in engaging contact against each other and to thus form a self-centering clearance-free coupling; - the sanding foot is provided with a third coupling part with a toothing; - an attachment workpiece processing part is connectable in engaging manner to the sanding foot, and is provided for this purpose with a fourth coupling part with a toothing which co-acts with the toothing of the third coupling part; - the toothing of the third coupling part and the toothing of the fourth coupling part are mutually engageable crown gears; - second clamping means are configured to clamp the crown gears (20, 26) of the third and the fourth coupling part (18, 24) in engaging contact against each other; - the number of teeth of the toothing of the first coupling part connected directly and/or indirectly to the drive shaft and the number of teeth of the toothing of the third coupling part of the first workpiece processing part differ such that they have one or more common whole numbers as divisor and one or more common differing whole numbers as divisor; - the drive shaft is rotatable reciprocally through an angular displacement relative to the housing by the drive; and - the sanding machine comprises at least two exchangeable attachment workpiece processing parts in a first embodiment (22a-1) and in a second embodiment (22a-2), wherein the orientation in which the crown gear of the fourth coupling part is arranged on the attachment workpiece processing part in the first embodiment (22a-1) differs from the orientation in which the crown gear of the fourth coupling part is arranged on the attachment workpiece processing part in the second embodiment (22a-2).