Restructuring Activities (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Restructuring Reserve [Roll Forward]
Beginning Balance	$ 2.0	$ 0.9
Acquisition	2.2	0.0
Provision	14.0	26.6
Less: Payments	13.2	25.5
Ending Balance	5.0	2.0	$ 0.9
Total Restructuring and Restructuring-Related Costs	14.0	26.6	21.6
Commercial Systems
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	1.9	6.3	9.5
Industrial Systems
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	1.9	8.7	7.2
Climate Solutions
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	0.8	3.7	2.2
Motion Control Solutions
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	9.4	7.9	2.7
Cost of Sales
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	12.2	18.2	10.7
Operating Expenses
Restructuring Reserve [Roll Forward]
Total Restructuring and Restructuring-Related Costs	1.8	8.4	10.9
Associate Termination Expenses
Restructuring Reserve [Roll Forward]
Restructuring costs	7.6	11.8	12.2
Associate Termination Expenses | Cost of Sales
Restructuring Reserve [Roll Forward]
Restructuring costs	6.4	6.2	5.7
Associate Termination Expenses | Operating Expenses
Restructuring Reserve [Roll Forward]
Restructuring costs	1.2	5.6	6.5
Facility Related Costs
Restructuring Reserve [Roll Forward]
Restructuring costs	4.5	14.8	9.4
Facility Related Costs | Cost of Sales
Restructuring Reserve [Roll Forward]
Restructuring costs	4.2	11.7	5.0
Facility Related Costs | Operating Expenses
Restructuring Reserve [Roll Forward]
Restructuring costs	0.3	3.1	4.4
Other Expenses
Restructuring Reserve [Roll Forward]
Restructuring costs	1.9	0.0	0.0
Other Expenses | Cost of Sales
Restructuring Reserve [Roll Forward]
Restructuring costs	1.6	0.3	0.0
Other Expenses | Operating Expenses
Restructuring Reserve [Roll Forward]
Restructuring costs	$ 0.3	$ (0.3)	$ 0.0