Segment Information (Schedule Change in Accounting Policy Related to LIFO) (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]
Gross Profit	$ 213.5	$ 221.6	$ 170.3	$ 203.3	$ 190.2	$ 201.9	$ 234.0	$ 234.6	$ 808.7	$ 860.7	$ 964.6
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
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	22.2	24.6	6.2	12.1	10.9	16.9	19.6	59.4		106.8
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
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	$ (14.9)	7.3	3.2	(0.1)	(4.4)	(2.6)	(0.1)	(5.9)		(13.0)
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