Business Segment Information - Schedule of Net Sales by Geographical Segments (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2021	Dec. 31, 2020
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	$ 1,791.7	$ 1,576.5
North America
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	1,611.3	1,339.9
Europe, Africa and Middle East
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	99.0	142.9
Rest of the World
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	81.4	93.7
Intersegment Eliminations
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	(2.5)	(7.1)
Intersegment Eliminations | North America
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	(2.5)	(7.1)
Access Equipment
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	833.3	562.4
Access Equipment | Operating Segments
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	833.5	563.7
Access Equipment | Operating Segments | North America
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	671.6	405.3
Access Equipment | Operating Segments | Europe, Africa and Middle East
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	86.1	74.4
Access Equipment | Operating Segments | Rest of the World
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	75.8	84.0
Access Equipment | Intersegment Eliminations
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	0.2	1.3
Defense
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	531.1	550.0
Defense | Operating Segments
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	531.5	550.3
Defense | Operating Segments | North America
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	523.4	494.2
Defense | Operating Segments | Europe, Africa and Middle East
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	8.0	55.3
Defense | Operating Segments | Rest of the World
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	0.1	0.8
Defense | Intersegment Eliminations
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	0.4	0.3
Fire & Emergency
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	217.0	269.8
Fire & Emergency | Operating Segments
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	218.6	273.9
Fire & Emergency | Operating Segments | North America
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	211.9	253.0
Fire & Emergency | Operating Segments | Europe, Africa and Middle East
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	4.1	13.0
Fire & Emergency | Operating Segments | Rest of the World
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	2.6	7.9
Fire & Emergency | Intersegment Eliminations
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	1.6	4.1
Commercial
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	210.2	194.2
Commercial | Operating Segments
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	210.6	195.7
Commercial | Operating Segments | North America
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	206.9	194.5
Commercial | Operating Segments | Europe, Africa and Middle East
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	0.8	0.2
Commercial | Operating Segments | Rest of the World
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	2.9	1.0
Commercial | Intersegment Eliminations
Revenues From External Customers And Long Lived Assets [Line Items]
Revenues	$ 0.4	$ 1.5