Restructuring Activities (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2021	Dec. 28, 2019	Dec. 29, 2018
Restructuring Reserve [Roll Forward]
Beginning Balance	$ 0.9	$ 0.2
Provision	26.6	21.6
Less: Payments	25.5	20.9
Ending Balance	2.0	0.9	$ 0.2
Restructuring Costs	26.6	21.6	7.6
Total Restructuring-Related Costs	0.0	0.0	0.1
Total Restructuring and Restructuring-Related Costs	26.6	21.6	7.7
Expected future restructuring charges	1.6
Commercial Systems
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	6.3	9.5	2.9
Industrial Systems
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	8.7	7.2	2.7
Climate Solutions
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	3.7	2.2	1.8
Power Transmission Solutions
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	7.9	2.7	0.3
Cost of Sales
Restructuring Reserve [Roll Forward]
Restructuring Costs	18.2	10.7	3.1
Total Restructuring-Related Costs	0.0	0.0	0.1
Total Restructuring and Restructuring-Related Costs	18.2	10.7	3.2
Operating Expenses
Restructuring Reserve [Roll Forward]
Restructuring Costs	8.4	10.9	4.5
Total Restructuring-Related Costs	0.0	0.0	0.0
Total Restructuring and Restructuring-Related Costs	8.4	10.9	4.5
Associate Termination Expenses
Restructuring Reserve [Roll Forward]
Restructuring Costs	11.8	12.2	0.3
Total Restructuring-Related Costs	0.0	0.0	0.1
Expected future restructuring charges	0.9
Associate Termination Expenses | Cost of Sales
Restructuring Reserve [Roll Forward]
Restructuring Costs	6.2	5.7	0.0
Total Restructuring-Related Costs	0.0	0.0	0.1
Associate Termination Expenses | Operating Expenses
Restructuring Reserve [Roll Forward]
Restructuring Costs	5.6	6.5	0.3
Total Restructuring-Related Costs	0.0	0.0	0.0
Facility Related Costs
Restructuring Reserve [Roll Forward]
Restructuring Costs	14.8	9.4	5.7
Expected future restructuring charges	0.7
Facility Related Costs | Cost of Sales
Restructuring Reserve [Roll Forward]
Restructuring Costs	11.7	5.0	2.3
Facility Related Costs | Operating Expenses
Restructuring Reserve [Roll Forward]
Restructuring Costs	3.1	4.4	3.4
Other Expenses
Restructuring Reserve [Roll Forward]
Restructuring Costs	0.0	0.0	1.6
Other Expenses | Cost of Sales
Restructuring Reserve [Roll Forward]
Restructuring Costs	0.3	0.0	0.8
Other Expenses | Operating Expenses
Restructuring Reserve [Roll Forward]
Restructuring Costs	$ (0.3)	$ 0.0	$ 0.8