Segment information - Net Sales by Geographic Regions and Markets (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Revenues from External Customers and Long-Lived Assets
Net sales	$ 3,474.4	$ 2,793.0	$ 3,087.1
Developed
Revenues from External Customers and Long-Lived Assets
Net sales	2,214.6	1,787.8	2,013.4
Emerging
Revenues from External Customers and Long-Lived Assets
Net sales	1,259.8	1,005.2	1,073.7
Power Transmission
Revenues from External Customers and Long-Lived Assets
Net sales	2,216.3	1,800.2	1,945.7
Power Transmission | U.S.
Revenues from External Customers and Long-Lived Assets
Net sales	621.8	538.3	580.4
Power Transmission | North America, excluding U.S.
Revenues from External Customers and Long-Lived Assets
Net sales	179.8	147.3	165.3
Power Transmission | United Kingdom (“U.K.”)
Revenues from External Customers and Long-Lived Assets
Net sales	50.2	44.3	43.6
Power Transmission | EMEA, excluding U.K.
Revenues from External Customers and Long-Lived Assets
Net sales	640.6	487.4	509.9
Power Transmission | East Asia and India
Revenues from External Customers and Long-Lived Assets
Net sales	308.6	251.8	288.6
Power Transmission | Greater China
Revenues from External Customers and Long-Lived Assets
Net sales	344.2	279.5	288.4
Power Transmission | South America
Revenues from External Customers and Long-Lived Assets
Net sales	71.1	51.6	69.5
Fluid Power
Revenues from External Customers and Long-Lived Assets
Net sales	1,258.1	992.8	1,141.4
Fluid Power | U.S.
Revenues from External Customers and Long-Lived Assets
Net sales	615.5	513.9	590.0
Fluid Power | North America, excluding U.S.
Revenues from External Customers and Long-Lived Assets
Net sales	193.8	146.9	175.9
Fluid Power | United Kingdom (“U.K.”)
Revenues from External Customers and Long-Lived Assets
Net sales	58.3	28.2	37.3
Fluid Power | EMEA, excluding U.K.
Revenues from External Customers and Long-Lived Assets
Net sales	198.8	151.0	173.6
Fluid Power | East Asia and India
Revenues from External Customers and Long-Lived Assets
Net sales	86.3	60.5	74.3
Fluid Power | Greater China
Revenues from External Customers and Long-Lived Assets
Net sales	67.8	66.9	57.8
Fluid Power | South America
Revenues from External Customers and Long-Lived Assets
Net sales	$ 37.6	$ 25.4	$ 32.5