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Shareholders' Equity (Narrative) (Details) (USD $)
In Millions, except Share data, unless otherwise specified
9 Months Ended 12 Months Ended
Sep. 27, 2014
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Apr. 29, 2013
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Treasury Stock, Shares, Acquired 500,000us-gaap_TreasuryStockSharesAcquired        
Treasury Stock Acquired, Average Cost Per Share $ 69.94us-gaap_TreasuryStockAcquiredAverageCostPerShare        
Payments for Repurchase of Common Stock $ 35.0us-gaap_PaymentsForRepurchaseOfCommonStock $ 35.0us-gaap_PaymentsForRepurchaseOfCommonStock $ 0us-gaap_PaymentsForRepurchaseOfCommonStock $ 0us-gaap_PaymentsForRepurchaseOfCommonStock  
Recognized share-based compensation expense   11.9us-gaap_ShareBasedCompensation 11.4us-gaap_ShareBasedCompensation 9.0us-gaap_ShareBasedCompensation  
Unrecognized compensation cost related to share-based compensation   21.9us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized      
Stock Issued During Period, Shares, New Issues   0us-gaap_StockIssuedDuringPeriodSharesNewIssues 0us-gaap_StockIssuedDuringPeriodSharesNewIssues 3,200,000us-gaap_StockIssuedDuringPeriodSharesNewIssues  
Vesting period, minimum   5 years      
Share-based compensation expected to recognize over a weighted average period, years   2 years 0 months 18 days      
Number of shares approved to be repurchased   3,000,000us-gaap_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased      
Share-based Compensation Arrangement by Share-based Payment Award, Expiration Period   10 years      
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
     
Share-based compensation expected to recognize over a weighted average period, years   2 years 11 months 12 days      
Restricted Stock [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Allocated Share-based Compensation Expense   1.5us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
     
Employee Service Share-based Compensation, Nonvested Awards, Total Compensation Cost Not yet Recognized, Share-based Awards Other than Options   0.4us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
     
Share-based compensation expected to recognize over a weighted average period, years   4 months 2 days      
Restricted Stock Units (RSUs) [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Allocated Share-based Compensation Expense   4.4us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
     
Employee Service Share-based Compensation, Nonvested Awards, Total Compensation Cost Not yet Recognized, Share-based Awards Other than Options   9.3us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
     
Share-based compensation expected to recognize over a weighted average period, years   1 year 9 months 18 days      
Performance Share Units [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Allocated Share-based Compensation Expense   1.0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
0.4us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Employee Service Share-based Compensation, Nonvested Awards, Total Compensation Cost Not yet Recognized, Share-based Awards Other than Options   $ 2.6us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
     
Share-based compensation expected to recognize over a weighted average period, years   1 year 11 months 23 days      
Share-based Compensation Arrangement by Share-based Payment Award, Performance Award Performance Period   3 years      
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost, Basis of Recognition, % of Target Payout   100.00%rbc_SharebasedCompensationArrangementbySharebasedPaymentAwardCompensationCostBasisofRecognitionofTargetPayout
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
     
Performance Share Units [Member] | Minimum [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based Compensation Arrangement by Share-based Payment Award, Performance Shares Term, Potential Payout as a Percentage of Target   0.00%rbc_SharebasedCompensationArrangementbySharebasedPaymentAwardPerformanceSharesTermPotentialPayoutasaPercentageofTarget
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MinimumMember
     
Performance Share Units [Member] | Maximum [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based Compensation Arrangement by Share-based Payment Award, Performance Shares Term, Potential Payout as a Percentage of Target   200.00%rbc_SharebasedCompensationArrangementbySharebasedPaymentAwardPerformanceSharesTermPotentialPayoutasaPercentageofTarget
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MaximumMember
     
Common Stock [Member] | 2013 Equity Incentive Plan [Member]          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Authorized shares of common stock         3,500,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_PlanNameAxis
= rbc_A2013EquityIncentivePlanMember
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonStockMember
Share available for future grant or payment under the various plans   3,000,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant
/ us-gaap_PlanNameAxis
= rbc_A2013EquityIncentivePlanMember
/ us-gaap_StatementClassOfStockAxis
= us-gaap_CommonStockMember