Segment Information (Schedule of Financial Information Attributable To The Reporting Segments) (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	Dec. 28, 2019	Sep. 28, 2019	Jun. 29, 2019	Mar. 30, 2019	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Segment Reporting Information [Line Items]
Net Sales	$ 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
Gross Profit	334.2	254.6	251.5	245.4	213.5	221.6	170.3	203.3					1,085.7	808.7	860.7
Operating Expenses													714.7	512.9	544.3
Goodwill Impairment	33.0												33.0	10.5	0.0
Gain (Loss) on sale of businesses													0.0	(0.1)	(44.7)
Asset Impairments													5.6	5.3	10.0
Income (Loss) from Operations	18.9	107.4	109.0	97.1	74.2	90.0	45.9	70.0					332.4	280.1	351.1
Depreciation and Amortization													170.6	131.4	134.5
Capital Expenditures													54.5	47.5	92.4
Commercial Systems
Segment Reporting Information [Line Items]
Net Sales	257.1	268.7	269.3	237.0	226.4	218.5	175.9	199.4					1,032.1	820.2	905.3
Gross Profit						61.4	42.3	50.7	$ 48.6	$ 53.6	$ 65.2	$ 65.5			232.9
Goodwill Impairment													0.0	0.0
Income (Loss) from Operations	16.2	30.4	25.4	27.5	22.2	24.6	6.2	12.1
Industrial Systems
Segment Reporting Information [Line Items]
Net Sales	146.7	148.0	145.2	136.4	139.8	138.8	120.6	129.6					576.3	528.8	575.4
Gross Profit						31.2	24.9	22.6	$ 24.0	$ 23.7	$ 27.8	$ 23.9			99.3
Goodwill Impairment													33.0	10.5
Income (Loss) from Operations	(27.3)	6.4	3.1	3.7	(14.9)	7.3	3.2	(0.1)
Climate Solutions
Segment Reporting Information [Line Items]
Net Sales	265.8	268.4	257.3	239.1	224.5	234.0	178.2	210.1					1,030.6	846.8	968.5
Goodwill Impairment													0.0	0.0
Income (Loss) from Operations	$ 47.2	$ 52.1	$ 46.5	$ 43.3	$ 41.3	$ 39.2	$ 20.0	$ 29.5
Motion Control Solutions
Segment Reporting Information [Line Items]
Net Sales													1,171.3	711.2	788.8
Goodwill Impairment													0.0	0.0
Intersegment Eliminations
Segment Reporting Information [Line Items]
Net Sales													138.5	111.5	104.5
Intersegment Eliminations | Commercial Systems
Segment Reporting Information [Line Items]
Net Sales													(88.7)	(62.5)	(46.9)
Intersegment Eliminations | Industrial Systems
Segment Reporting Information [Line Items]
Net Sales													(26.6)	(27.7)	(35.9)
Intersegment Eliminations | Climate Solutions
Segment Reporting Information [Line Items]
Net Sales													(19.1)	(18.8)	(17.4)
Intersegment Eliminations | Motion Control Solutions
Segment Reporting Information [Line Items]
Net Sales													(4.1)	(2.5)	(4.3)
Operating Segments | Commercial Systems
Segment Reporting Information [Line Items]
Net Sales													1,120.8	882.7	952.2
Gross Profit													262.4	212.7	236.6
Operating Expenses													161.1	144.9	162.4
Goodwill Impairment													0.0	0.0
Gain (Loss) on sale of businesses														(0.1)	(39.3)
Asset Impairments													1.8	2.8	6.7
Income (Loss) from Operations													99.5	65.1	106.8
Depreciation and Amortization													29.9	32.6	34.6
Capital Expenditures													17.8	15.3	29.9
Operating Segments | Industrial Systems
Segment Reporting Information [Line Items]
Net Sales													602.9	556.5	611.3
Gross Profit													106.9	97.8	95.6
Operating Expenses													88.0	91.6	107.6
Goodwill Impairment													33.0	10.5
Gain (Loss) on sale of businesses														0.0	0.1
Asset Impairments													0.0	0.2	0.9
Income (Loss) from Operations													(14.1)	(4.5)	(13.0)
Depreciation and Amortization													23.2	23.9	24.4
Capital Expenditures													9.5	8.1	21.0
Operating Segments | Climate Solutions
Segment Reporting Information [Line Items]
Net Sales													1,049.7	865.6	985.9
Gross Profit													305.1	246.8	269.8
Operating Expenses													115.5	115.5	110.6
Goodwill Impairment													0.0	0.0
Gain (Loss) on sale of businesses														0.0	(6.0)
Asset Impairments													0.5	1.3	1.3
Income (Loss) from Operations													189.1	130.0	163.9
Depreciation and Amortization													16.5	19.6	19.8
Capital Expenditures													11.7	12.1	23.3
Operating Segments | Motion Control Solutions
Segment Reporting Information [Line Items]
Net Sales													1,175.4	713.7	793.1
Gross Profit													411.3	251.4	258.7
Operating Expenses													350.1	160.9	163.7
Goodwill Impairment													0.0	0.0
Gain (Loss) on sale of businesses														0.0	0.5
Asset Impairments													3.3	1.0	1.1
Income (Loss) from Operations													57.9	89.5	93.4
Depreciation and Amortization													101.0	55.3	55.7
Capital Expenditures													$ 15.5	$ 12.0	$ 18.2