Reporting Segment And Geographic Information Reporting Segment And Geographic Information - Schedule of Revised Operating Income (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2016	Jan. 02, 2015	Jan. 03, 2014
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)	$ 154.4	$ 260.8	$ 251.7
Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Allocated Share-based Compensation Expense		(25.8)	(22.6)
Operating Segments [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)	459.9	544.2	537.6
Operating Segments [Member] | Scenario, Adjustment [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		544.2	537.6
Operating Segments [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		518.4	515.0
Field Solutions [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Allocated Share-based Compensation Expense		(3.6)	(3.1)
Field Solutions [Member] | Operating Segments [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)	108.6	137.8	176.2
Field Solutions [Member] | Operating Segments [Member] | Scenario, Adjustment [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		137.8	176.2
Field Solutions [Member] | Operating Segments [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		134.2	173.1
Mobile Solutions [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Allocated Share-based Compensation Expense		(5.1)	(4.0)
Mobile Solutions [Member] | Operating Segments [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)	85.6	78.0	68.0
Mobile Solutions [Member] | Operating Segments [Member] | Scenario, Adjustment [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		78.0	68.0
Mobile Solutions [Member] | Operating Segments [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		72.9	64.0
Advanced Devices [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Allocated Share-based Compensation Expense		(1.9)	(3.2)
Advanced Devices [Member] | Operating Segments [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)	46.9	44.3	29.8
Advanced Devices [Member] | Operating Segments [Member] | Scenario, Adjustment [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		44.3	29.8
Advanced Devices [Member] | Operating Segments [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		42.4	26.6
Engineering And Construction [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Allocated Share-based Compensation Expense		(15.2)	(12.3)
Engineering And Construction [Member] | Operating Segments [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)	$ 218.8	284.1	263.6
Engineering And Construction [Member] | Operating Segments [Member] | Scenario, Adjustment [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		284.1	263.6
Engineering And Construction [Member] | Operating Segments [Member] | Scenario, Previously Reported [Member]
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Operating Income (Loss)		$ 268.9	$ 251.3