Accounting Policies (Disaggregation of Revenue) (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 01, 2022	Oct. 02, 2021	Jul. 03, 2021	Apr. 03, 2021	Jan. 02, 2021	Sep. 26, 2020	Jun. 27, 2020	Mar. 28, 2020	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Disaggregation of Revenue [Line Items]
Revenue	$ 1,216.6	$ 892.7	$ 886.9	$ 814.1	$ 780.5	$ 758.2	$ 634.1	$ 734.2	$ 3,810.3	$ 2,907.0	$ 3,238.0
North America
Disaggregation of Revenue [Line Items]
Revenue									2,775.1	2,183.4	2,445.0
Asia
Disaggregation of Revenue [Line Items]
Revenue									463.0	331.0	342.3
Europe
Disaggregation of Revenue [Line Items]
Revenue									361.5	247.6	316.7
Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									210.7	145.0	134.0
Commercial Systems
Disaggregation of Revenue [Line Items]
Revenue	257.1	268.7	269.3	237.0	226.4	218.5	175.9	199.4	1,032.1	820.2	905.3
Commercial Systems | North America
Disaggregation of Revenue [Line Items]
Revenue									696.0	566.9	643.0
Commercial Systems | Asia
Disaggregation of Revenue [Line Items]
Revenue									182.3	124.9	107.2
Commercial Systems | Europe
Disaggregation of Revenue [Line Items]
Revenue									102.7	86.1	135.5
Commercial Systems | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									51.1	42.3	19.6
Industrial Systems
Disaggregation of Revenue [Line Items]
Revenue	146.7	148.0	145.2	136.4	139.8	138.8	120.6	129.6	576.3	528.8	575.4
Industrial Systems | North America
Disaggregation of Revenue [Line Items]
Revenue									296.2	291.4	313.5
Industrial Systems | Asia
Disaggregation of Revenue [Line Items]
Revenue									186.7	150.9	167.0
Industrial Systems | Europe
Disaggregation of Revenue [Line Items]
Revenue									46.4	44.8	49.2
Industrial Systems | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									47.0	41.7	45.7
Climate Solutions
Disaggregation of Revenue [Line Items]
Revenue	$ 265.8	$ 268.4	$ 257.3	$ 239.1	$ 224.5	$ 234.0	$ 178.2	$ 210.1	1,030.6	846.8	968.5
Climate Solutions | North America
Disaggregation of Revenue [Line Items]
Revenue									905.9	752.7	848.6
Climate Solutions | Asia
Disaggregation of Revenue [Line Items]
Revenue									33.7	27.7	37.7
Climate Solutions | Europe
Disaggregation of Revenue [Line Items]
Revenue									43.6	30.3	40.5
Climate Solutions | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									47.4	36.1	41.7
Motion Control Solutions
Disaggregation of Revenue [Line Items]
Revenue									1,171.3	711.2	788.8
Motion Control Solutions | North America
Disaggregation of Revenue [Line Items]
Revenue									877.0	572.4	639.9
Motion Control Solutions | Asia
Disaggregation of Revenue [Line Items]
Revenue									60.3	27.5	30.4
Motion Control Solutions | Europe
Disaggregation of Revenue [Line Items]
Revenue									168.8	86.4	91.5
Motion Control Solutions | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									$ 65.2	$ 24.9	$ 27.0