Accounting Policies (Disaggregation of Revenue) (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Jan. 02, 2021	Sep. 26, 2020	Jun. 27, 2020	Mar. 28, 2020	Dec. 28, 2019	Sep. 28, 2019	Jun. 29, 2019	Mar. 30, 2019	Jan. 02, 2021	Dec. 28, 2019	Dec. 29, 2018
Disaggregation of Revenue [Line Items]
Revenue	$ 780.5	$ 758.2	$ 634.1	$ 734.2	$ 738.2	$ 772.3	$ 873.7	$ 853.8	$ 2,907.0	$ 3,238.0	$ 3,645.6
North America
Disaggregation of Revenue [Line Items]
Revenue									2,183.4	2,445.0	2,751.9
Asia
Disaggregation of Revenue [Line Items]
Revenue									331.0	342.3	401.1
Europe
Disaggregation of Revenue [Line Items]
Revenue									247.6	316.7	324.6
Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									145.0	134.0	168.0
Commercial Systems
Disaggregation of Revenue [Line Items]
Revenue	226.4	218.5	175.9	199.4	202.0	214.8	246.3	242.2	820.2	905.3	1,110.9
Commercial Systems | North America
Disaggregation of Revenue [Line Items]
Revenue									566.9	643.0	813.6
Commercial Systems | Asia
Disaggregation of Revenue [Line Items]
Revenue									124.9	107.2	142.7
Commercial Systems | Europe
Disaggregation of Revenue [Line Items]
Revenue									86.1	135.5	122.1
Commercial Systems | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									42.3	19.6	32.5
Industrial Systems
Disaggregation of Revenue [Line Items]
Revenue	139.8	138.8	120.6	129.6	138.0	143.8	155.5	138.1	528.8	575.4	671.1
Industrial Systems | North America
Disaggregation of Revenue [Line Items]
Revenue									291.4	313.5	360.0
Industrial Systems | Asia
Disaggregation of Revenue [Line Items]
Revenue									150.9	167.0	194.8
Industrial Systems | Europe
Disaggregation of Revenue [Line Items]
Revenue									44.8	49.2	55.1
Industrial Systems | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									41.7	45.7	61.2
Climate Solutions
Disaggregation of Revenue [Line Items]
Revenue	224.5	234.0	178.2	210.1	206.4	230.9	267.9	263.3	846.8	968.5	1,024.8
Climate Solutions | North America
Disaggregation of Revenue [Line Items]
Revenue									752.7	848.6	891.9
Climate Solutions | Asia
Disaggregation of Revenue [Line Items]
Revenue									27.7	37.7	39.5
Climate Solutions | Europe
Disaggregation of Revenue [Line Items]
Revenue									30.3	40.5	50.5
Climate Solutions | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									36.1	41.7	42.9
Power Transmission Solutions
Disaggregation of Revenue [Line Items]
Revenue	$ 189.8	$ 166.9	$ 159.4	$ 195.1	$ 191.8	$ 182.8	$ 204.0	$ 210.2	711.2	788.8	838.8
Power Transmission Solutions | North America
Disaggregation of Revenue [Line Items]
Revenue									572.4	639.9	686.4
Power Transmission Solutions | Asia
Disaggregation of Revenue [Line Items]
Revenue									27.5	30.4	24.1
Power Transmission Solutions | Europe
Disaggregation of Revenue [Line Items]
Revenue									86.4	91.5	96.9
Power Transmission Solutions | Rest-of-World
Disaggregation of Revenue [Line Items]
Revenue									$ 24.9	$ 27.0	$ 31.4