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Retirement Plans (Narrative) (Details) (USD $)
In Millions, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Accumulated benefit obligation 182.3us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation 160.1us-gaap_DefinedBenefitPlanAccumulatedBenefitObligation  
Projected benefit obligation   50.4us-gaap_DefinedBenefitPlanPensionPlansWithAccumulatedBenefitObligationsInExcessOfPlanAssetsAggregateProjectedBenefitObligation  
Accumulated benefit obligation   43.0us-gaap_DefinedBenefitPlanPensionPlansWithAccumulatedBenefitObligationsInExcessOfPlanAssetsAggregateAccumulatedBenefitObligation  
Fair value of plan assets   9.1us-gaap_DefinedBenefitPlanPensionPlansWithAccumulatedBenefitObligationsInExcessOfPlanAssetsAggregateFairValueOfPlanAssets  
Defined Benefit Plan, Amortization of Net Prior Service Cost (Credit) 0.2us-gaap_DefinedBenefitPlanFutureAmortizationOfPriorServiceCostCredit    
Defined benefit plan compensation increase assumption 0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingBenefitObligationRateOfCompensationIncrease 0.00%us-gaap_DefinedBenefitPlanAssumptionsUsedCalculatingBenefitObligationRateOfCompensationIncrease  
Defined Benefit Plan, Contributions by Employer 3.1us-gaap_DefinedBenefitPlanContributionsByEmployer 5.5us-gaap_DefinedBenefitPlanContributionsByEmployer  
Expected contribution to defined benefit pension plans 3.3us-gaap_DefinedBenefitPlansEstimatedFutureEmployerContributionsInCurrentFiscalYear    
Pension and Other Postretirement Benefit Plans, Amounts that Will be Amortized from Accumulated Other Comprehensive Income (Loss) in Next Fiscal Year 4.6us-gaap_DefinedBenefitPlanAmountToBeAmortizedFromAccumulatedOtherComprehensiveIncomeLossNextFiscalYear    
United States Pension Plans of US Entity, Defined Benefit [Member]      
Defined Benefit Plan, Other Information 8.8 9.1 9.8
Foreign Pension Plans, Defined Benefit [Member]      
Defined Benefit Plan, Contributions by Employer 12.6us-gaap_DefinedBenefitPlanContributionsByEmployer
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_ForeignPensionPlansDefinedBenefitMember
12.4us-gaap_DefinedBenefitPlanContributionsByEmployer
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_ForeignPensionPlansDefinedBenefitMember
12.0us-gaap_DefinedBenefitPlanContributionsByEmployer
/ us-gaap_DefinedBenefitPlansDisclosuresDefinedBenefitPlansAxis
= us-gaap_ForeignPensionPlansDefinedBenefitMember
Real Estate [Member]      
Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value 6.2us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_InvestmentTypeAxis
= us-gaap_RealEstateMember
5.5us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_InvestmentTypeAxis
= us-gaap_RealEstateMember
 
Fair Value, Inputs, Level 3 [Member] | Minimum [Member]      
Fair Value Inputs, Exit Capitalization Rate 5.30%rbc_FairValueInputsExitCapitalizationRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
5.40%rbc_FairValueInputsExitCapitalizationRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
 
Fair Value Inputs, Discount Rate 6.80%us-gaap_FairValueInputsDiscountRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
6.90%us-gaap_FairValueInputsDiscountRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
 
Fair Value, Inputs, Level 3 [Member] | Maximum [Member]      
Fair Value Inputs, Exit Capitalization Rate 7.50%rbc_FairValueInputsExitCapitalizationRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MaximumMember
7.60%rbc_FairValueInputsExitCapitalizationRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MaximumMember
 
Fair Value Inputs, Discount Rate 9.50%us-gaap_FairValueInputsDiscountRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MaximumMember
9.70%us-gaap_FairValueInputsDiscountRate
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
/ us-gaap_RangeAxis
= us-gaap_MaximumMember