Taxes Based on Income (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 01, 2017	Jul. 02, 2016	Jul. 01, 2017	Jul. 02, 2016
Taxes Based on Income
Income before taxes	$ 149.5	$ 99.3	$ 285.4	$ 222.8
Provision for income taxes	$ 28.6	$ 19.3	$ 52.3	$ 53.2
Effective tax rate (as a percent)	19.10%	19.40%	18.30%	23.90%
Tax benefit from effective settlements of certain foreign tax examinations and changes in our judgment about tax filing positions in certain foreign jurisdictions as a result of new information gained from our interactions with tax authorities	$ 3.4	$ 5.0	$ 3.4	$ 6.0
Tax benefit due to decreases in certain tax reserves as a result of closing tax years	3.1	0.7	4.6	3.3
Net benefit corresponding to the adoption of an accounting guidance update related to stock-based payments	0.6		13.3
Tax effect of the tax deductions in excess of compensation cost related to the exercise of nonqualified stock options and vesting of other stock-based compensation awards recognized in capital in excess of par value		0.2		7.1
Tax benefit from the release of valuation allowances against certain deferred tax assets in a foreign jurisdiction associated with a structural simplification approved by the tax authority		$ 6.7		$ 6.7
Reasonably possible decrease in uncertain tax positions, including interest and penalties, during the next 12 months	$ 23.0		$ 23.0