Segment Information (Schedule of Financial Information Attributable To The Reporting Segments) (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
Segment Reporting Information [Line Items]
Net Sales	$ 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
Gross Profit	213.5	221.6	170.3	203.3	190.2	201.9	234.0	234.6	808.7	860.7	964.6
Operating Expenses									512.9	544.3	599.4
Goodwill Impairment									10.5	0.0	9.5
Asset Impairments									5.3	10.0	8.7
(Gain) Loss on Sale of Businesses								(41.2)	(0.1)	(44.7)	0.0
Income (Loss) from Operations	74.2	90.0	45.9	70.0	61.7	72.8	96.0	120.6	280.1	351.1	347.0
Depreciation and Amortization									131.4	134.5	142.4
Capital Expenditures									47.5	92.4	77.6
Commercial Systems
Segment Reporting Information [Line Items]
Net Sales	226.4	218.5	175.9	199.4	202.0	214.8	246.3	242.2	820.2	905.3	1,110.9
Gross Profit		61.4	42.3	50.7	48.6	53.6	65.2	65.5		232.9
Goodwill Impairment									0.0
Income (Loss) from Operations	22.2	24.6	6.2	12.1	10.9	16.9	19.6	59.4		106.8
Industrial Systems
Segment Reporting Information [Line Items]
Net Sales	139.8	138.8	120.6	129.6	138.0	143.8	155.5	138.1	528.8	575.4	671.1
Gross Profit		31.2	24.9	22.6	24.0	23.7	27.8	23.9		99.3
Goodwill Impairment									10.5
Income (Loss) from Operations	(14.9)	7.3	3.2	(0.1)	(4.4)	(2.6)	(0.1)	(5.9)		(13.0)
Climate Solutions
Segment Reporting Information [Line Items]
Net Sales	224.5	234.0	178.2	210.1	206.4	230.9	267.9	263.3	846.8	968.5	1,024.8
Goodwill Impairment									0.0
Income (Loss) from Operations	41.3	39.2	20.0	29.5	35.7	37.6	51.7	38.9
Power Transmission Solutions
Segment Reporting Information [Line Items]
Net Sales	189.8	166.9	159.4	195.1	191.8	182.8	204.0	210.2	711.2	788.8	838.8
Goodwill Impairment									0.0
Income (Loss) from Operations	$ 25.6	$ 18.9	$ 16.5	$ 28.5	$ 19.5	$ 20.9	$ 24.8	$ 28.2
Intersegment Eliminations
Segment Reporting Information [Line Items]
Net Sales									111.5	104.5	125.4
Intersegment Eliminations | Commercial Systems
Segment Reporting Information [Line Items]
Net Sales									(62.5)	(46.9)	(47.3)
Intersegment Eliminations | Industrial Systems
Segment Reporting Information [Line Items]
Net Sales									(27.7)	(35.9)	(31.9)
Intersegment Eliminations | Climate Solutions
Segment Reporting Information [Line Items]
Net Sales									(18.8)	(17.4)	(22.1)
Intersegment Eliminations | Power Transmission Solutions
Segment Reporting Information [Line Items]
Net Sales									(2.5)	(4.3)	(24.1)
Operating Segments | Commercial Systems
Segment Reporting Information [Line Items]
Net Sales									882.7	952.2	1,158.2
Gross Profit									213.8	236.6	287.0
Operating Expenses									144.9	162.4	184.8
Goodwill Impairment									0.0		0.0
Asset Impairments									2.8	6.7	0.0
(Gain) Loss on Sale of Businesses									(0.1)	(39.3)
Income (Loss) from Operations									66.2	106.8	102.2
Depreciation and Amortization									32.6	34.6	40.3
Capital Expenditures									15.3	29.9	24.6
Operating Segments | Industrial Systems
Segment Reporting Information [Line Items]
Net Sales									556.5	611.3	703.0
Gross Profit									96.7	95.6	136.4
Operating Expenses									91.6	107.6	111.6
Goodwill Impairment									10.5		0.0
Asset Impairments									0.2	0.9	0.0
(Gain) Loss on Sale of Businesses									0.0	0.1
Income (Loss) from Operations									(5.6)	(13.0)	24.8
Depreciation and Amortization									23.9	24.4	26.7
Capital Expenditures									8.1	21.0	17.2
Operating Segments | Climate Solutions
Segment Reporting Information [Line Items]
Net Sales									865.6	985.9	1,046.9
Gross Profit									246.8	269.8	262.7
Operating Expenses									115.5	110.6	128.9
Goodwill Impairment									0.0		9.5
Asset Impairments									1.3	1.3	8.7
(Gain) Loss on Sale of Businesses									0.0	(6.0)
Income (Loss) from Operations									130.0	163.9	115.6
Depreciation and Amortization									19.6	19.8	21.0
Capital Expenditures									12.1	23.3	17.7
Operating Segments | Power Transmission Solutions
Segment Reporting Information [Line Items]
Net Sales									713.7	793.1	862.9
Gross Profit									251.4	258.7	278.5
Operating Expenses									160.9	163.7	174.1
Goodwill Impairment									0.0		0.0
Asset Impairments									1.0	1.1	0.0
(Gain) Loss on Sale of Businesses									0.0	0.5
Income (Loss) from Operations									89.5	93.4	104.4
Depreciation and Amortization									55.3	55.7	54.4
Capital Expenditures									$ 12.0	$ 18.2	$ 18.1