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Shareholders' Equity (Schedule Of Share-Based Compensation Activity) (Details) (Options and SAR's [Member], USD $)
In Millions, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Options and SAR's [Member]
     
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Employee Service Share-based Compensation, Nonvested Awards, Total Compensation Cost Not yet Recognized, Share-based Awards Other than Options $ 11.3us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
   
Total intrinsic value of share-based incentive awards exercised 5.2us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
4.0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
11.1us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
Cash received from stock option exercises 1.9us-gaap_EmployeeServiceShareBasedCompensationCashReceivedFromExerciseOfStockOptions
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
1.5us-gaap_EmployeeServiceShareBasedCompensationCashReceivedFromExerciseOfStockOptions
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
4.2us-gaap_EmployeeServiceShareBasedCompensationCashReceivedFromExerciseOfStockOptions
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
Income tax benefit from the exercise of stock options 2.0us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
0.8us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
2.2us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitRealizedFromExerciseOfStockOptions
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
Total fair value of share-based incentive awards vested $ 5.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
$ 8.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
$ 6.6us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember