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Shareholders' Equity Stockholders' Equity Assumptions Used in Black Scholes valuation for Options and SAR's (Details) (USD $)
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Per share weighted average fair value of grants $ 28.01us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 23.01us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue $ 22.45us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
Options and SAR's [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Risk-free interest rate 2.00%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
1.10%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
1.30%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
Expected life (years) 7 years 7 years 7 years
Expected volatility 37.70%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
38.50%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
37.60%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
Expected dividend yield 1.20%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
1.20%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember
1.20%us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate
/ us-gaap_AwardTypeAxis
= rbc_OptionsandSARsMember