Sum of the carrying amounts as of the balance sheet date of all assets that are recognized. Assets are probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

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Name:	us-gaap_Assets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Segment Information (Narrative) (Details) $ in Millions	12 Months Ended
Segment Information (Narrative) (Details) $ in Millions	Jan. 02, 2021 USD ($) segment	Dec. 28, 2019 USD ($)	Dec. 29, 2018
Segment Reporting Information [Line Items]
Number of operating segments (in segment) \| segment	4
Assets	$ 4,589.0	$ 4,430.7
Commercial Systems
Segment Reporting Information [Line Items]
Assets	1,319.6	1,203.9
Commercial Systems \| LIFO Policy Change
Segment Reporting Information [Line Items]
Assets		5.4
Industrial Systems
Segment Reporting Information [Line Items]
Assets	$ 837.5	797.4
Industrial Systems \| LIFO Policy Change
Segment Reporting Information [Line Items]
Assets		$ 5.4
Geographic Concentration Risk \| Sales Revenue, Net \| United States
Segment Reporting Information [Line Items]
Concentration risk	64.80%	64.00%	65.90%