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Related Party Transactions (Details) (USD $)
In Millions, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Related Party Transaction [Line Items]      
Fees and Commissions, Other $ 5.3us-gaap_FeesAndCommissionsOther $ 0us-gaap_FeesAndCommissionsOther $ 0us-gaap_FeesAndCommissionsOther
Elco Group B.V. [Member]      
Related Party Transaction [Line Items]      
Amount payable to an entity related to acquisition 22.3us-gaap_DueToRelatedPartiesCurrentAndNoncurrent
/ us-gaap_RelatedPartyTransactionsByRelatedPartyAxis
= rbc_MexicobasedelectricalproductsMember
   
Acquisition to be paid in semi-annual payments $ 10.5rbc_BusinessAcquisitionCostOfAcquiredEntityCashToBePaidInSemiAnnualPayments
/ us-gaap_RelatedPartyTransactionsByRelatedPartyAxis
= rbc_MexicobasedelectricalproductsMember