Accounting Policies (Narrative) (Details)	3 Months Ended								12 Months Ended
	Jan. 02, 2021 USD ($)	Sep. 26, 2020 USD ($)	Jun. 27, 2020 USD ($)	Mar. 28, 2020 USD ($)	Dec. 28, 2019 USD ($)	Sep. 28, 2019 USD ($)	Jun. 29, 2019 USD ($)	Mar. 30, 2019 USD ($)	Jan. 02, 2021 USD ($) segment	Dec. 28, 2019 USD ($)	Dec. 29, 2018 USD ($)	Dec. 21, 2026	Dec. 29, 2019 USD ($)	Dec. 30, 2018 USD ($)	Dec. 30, 2017 USD ($)
Property, Plant and Equipment [Line Items]
Number of operating segments (in segment) | segment									4
Payment terms									due upon delivery to 120 days after delivery
Amortization period	12 months								12 months
Research and development costs									$ 34,700,000	$ 22,500,000	$ 29,300,000
Impairment of long-lived assets									5,300,000	5,100,000
Goodwill	$ 1,518,200,000				$ 1,501,300,000				1,518,200,000	1,501,300,000	1,509,200,000
Net Sales	780,500,000	$ 758,200,000	$ 634,100,000	$ 734,200,000	738,200,000	$ 772,300,000	$ 873,700,000	$ 853,800,000	2,907,000,000.0	3,238,000,000.0	3,645,600,000
Long-lived assets	555,500,000				605,000,000.0				555,500,000	605,000,000.0
Allowance for doubtful accounts receivable	18,300,000				9,700,000				18,300,000	9,700,000
Decrease to retained earnings	(2,577,000,000.0)				(2,380,400,000)				(2,577,000,000.0)	(2,380,400,000)	(2,338,500,000)				$ (2,354,700,000)
Right-of-use asset	73,400,000				71,000,000.0				73,400,000	71,000,000.0
Lease liabilities	76,700,000								76,700,000
Accounting Standards Update 2016-02
Property, Plant and Equipment [Line Items]
Right-of-use asset														$ 93,000,000.0
Lease liabilities														$ 93,000,000.0
Forecast | Postretirement Health Coverage
Property, Plant and Equipment [Line Items]
Health care cost trend rate, 2026												4.50%
Global Industrial Motors
Property, Plant and Equipment [Line Items]
Goodwill	114,900,000								114,900,000
Commercial Air Moving
Property, Plant and Equipment [Line Items]
Goodwill	43,800,000								43,800,000
Adjustment
Property, Plant and Equipment [Line Items]
Allowance for doubtful accounts receivable													$ 3,400,000
Decrease to retained earnings					2,700,000					2,700,000					0
Power Transmission Solutions
Property, Plant and Equipment [Line Items]
Goodwill	590,400,000				572,700,000				590,400,000	572,700,000	579,700,000
Net Sales	189,800,000	$ 166,900,000	$ 159,400,000	$ 195,100,000	191,800,000	$ 182,800,000	$ 204,000,000.0	$ 210,200,000	711,200,000	788,800,000	838,800,000
Disposal Group, Disposed of by Sale, Not Discontinued Operations
Property, Plant and Equipment [Line Items]
Long-lived assets					5,100,000					5,100,000
Customer Relationships | Hermetic Climate | Disposal Group, Disposed of by Sale, Not Discontinued Operations
Property, Plant and Equipment [Line Items]
Asset Impairments									0	4,900,000
Retained Earnings
Property, Plant and Equipment [Line Items]
Decrease to retained earnings	$ (2,010,700,000)				(1,886,700,000)				$ (2,010,700,000)	(1,886,700,000)	$ (1,777,900,000)				(1,611,600,000)
Retained Earnings | Adjustment
Property, Plant and Equipment [Line Items]
Decrease to retained earnings					$ 2,700,000					$ 2,700,000			$ 2,700,000		$ (4,600,000)