Segment Information (Schedule Change in Accounting Policy Related to LIFO) (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]
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
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
Commercial Systems
Segment Reporting Information [Line Items]
Gross Profit						61.4	42.3	50.7	$ 48.6	$ 53.6	$ 65.2	$ 65.5			232.9
Income (Loss) from Operations	16.2	30.4	25.4	27.5	22.2	24.6	6.2	12.1
Commercial Systems | Adjustment
Segment Reporting Information [Line Items]
Gross Profit						(0.7)	0.0	(0.4)	3.0	0.3	(1.2)	1.6			3.7
Commercial Systems | Adjusted balance
Segment Reporting Information [Line Items]
Gross Profit						60.7	42.3	50.4	51.6	53.9	64.0	67.1			236.6
Income (Loss) from Operations						24.6	6.2	12.1	10.9	16.9	19.6	59.4			106.8
Industrial Systems
Segment Reporting Information [Line Items]
Gross Profit						31.2	24.9	22.6	24.0	23.7	27.8	23.9			99.3
Income (Loss) from Operations	$ (27.3)	$ 6.4	$ 3.1	$ 3.7	$ (14.9)	7.3	3.2	(0.1)
Industrial Systems | Adjustment
Segment Reporting Information [Line Items]
Gross Profit						0.7	0.0	0.4	(3.0)	(0.3)	1.2	(1.6)			(3.7)
Industrial Systems | Adjusted balance
Segment Reporting Information [Line Items]
Gross Profit						31.9	24.8	23.0	21.0	23.4	29.0	22.3			95.6
Income (Loss) from Operations						$ 7.3	$ 3.2	$ (0.1)	$ (4.4)	$ (2.6)	$ (0.1)	$ (5.9)			$ (13.0)