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Subsequent Event (Details) (USD $)
3 Months Ended 12 Months Ended 0 Months Ended
Jan. 03, 2015
Sep. 27, 2014
Jun. 28, 2014
Mar. 29, 2014
Dec. 28, 2013
Sep. 28, 2013
Jun. 29, 2013
Mar. 30, 2013
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Jan. 30, 2015
Goodwill $ 1,004,000,000us-gaap_Goodwill       $ 1,081,900,000us-gaap_Goodwill       $ 1,004,000,000us-gaap_Goodwill $ 1,081,900,000us-gaap_Goodwill $ 1,151,000,000us-gaap_Goodwill  
New Credit Facility 500,000,000us-gaap_LineOfCredit               500,000,000us-gaap_LineOfCredit      
Sales Revenue, Goods, Net 775,600,000us-gaap_SalesRevenueGoodsNet 829,800,000us-gaap_SalesRevenueGoodsNet 850,400,000us-gaap_SalesRevenueGoodsNet 801,200,000us-gaap_SalesRevenueGoodsNet 727,200,000us-gaap_SalesRevenueGoodsNet 768,200,000us-gaap_SalesRevenueGoodsNet 822,000,000us-gaap_SalesRevenueGoodsNet 778,200,000us-gaap_SalesRevenueGoodsNet 3,257,100,000us-gaap_SalesRevenueGoodsNet 3,095,700,000us-gaap_SalesRevenueGoodsNet 3,166,900,000us-gaap_SalesRevenueGoodsNet  
Business Acquisition, Pro Forma Revenue                 3,291,200,000us-gaap_BusinessAcquisitionsProFormaRevenue 3,240,400,000us-gaap_BusinessAcquisitionsProFormaRevenue 3,328,800,000us-gaap_BusinessAcquisitionsProFormaRevenue  
Business Acquisition, Pro Forma Net Income (Loss)                 28,800,000us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss 123,800,000us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss 202,400,000us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss  
Basic $ (2,610,000.00)us-gaap_EarningsPerShareBasic $ 1,060,000.00us-gaap_EarningsPerShareBasic $ 1,240,000.00us-gaap_EarningsPerShareBasic $ 970,000.00us-gaap_EarningsPerShareBasic $ (740,000.00)us-gaap_EarningsPerShareBasic $ 1,170,000.00us-gaap_EarningsPerShareBasic $ 1,140,000.00us-gaap_EarningsPerShareBasic $ 1,100,000.00us-gaap_EarningsPerShareBasic $ 0.69us-gaap_EarningsPerShareBasic $ 2.66us-gaap_EarningsPerShareBasic $ 4.68us-gaap_EarningsPerShareBasic  
Business Acquisition, Pro Forma Earnings Per Share, Basic                 $ 0.64us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic $ 2.75us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic $ 0us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic  
Earnings Per Share, Diluted $ (2,610,000.00)us-gaap_EarningsPerShareDiluted $ 1,050,000.00us-gaap_EarningsPerShareDiluted $ 1,240,000.00us-gaap_EarningsPerShareDiluted $ 960,000.00us-gaap_EarningsPerShareDiluted $ (740,000.00)us-gaap_EarningsPerShareDiluted $ 1,160,000.00us-gaap_EarningsPerShareDiluted $ 1,130,000.00us-gaap_EarningsPerShareDiluted $ 1,090,000.00us-gaap_EarningsPerShareDiluted $ 0.69us-gaap_EarningsPerShareDiluted $ 2.64us-gaap_EarningsPerShareDiluted $ 4.64us-gaap_EarningsPerShareDiluted  
Business Acquisition, Pro Forma Earnings Per Share, Diluted                 $ 0.64us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted $ 2.73us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted $ 0us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted  
PTS Member [Domain]                        
Sales Revenue, Goods, Net                 607,300,000us-gaap_SalesRevenueGoodsNet
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
     
Business Acquisition, Pro Forma Revenue                 3,864,400,000us-gaap_BusinessAcquisitionsProFormaRevenue
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
     
Business Acquisition, Pro Forma Net Income (Loss)                 47,000,000us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
     
Basic                 $ 0.69us-gaap_EarningsPerShareBasic
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
     
Business Acquisition, Pro Forma Earnings Per Share, Basic                 $ 1.04us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
     
Earnings Per Share, Diluted                 $ 0.69us-gaap_EarningsPerShareDiluted
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
     
Business Acquisition, Pro Forma Earnings Per Share, Diluted                 $ 1.04us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
     
PTS Member [Domain] | Subsequent Event [Member]                        
Cash and Equivalents                       1,400,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Current Assets                       3,200,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Receivables                       71,300,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Inventory                       102,800,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Property, Plant, and Equipment                       1,384,000,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentAssets
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Assets                       1,561,300,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Current Liabilities, Other                       76,600,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesOther
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Noncurrent Liabilities, Other                       82,700,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Net assets acquired                       1,402,000,000,000us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet
/ us-gaap_BusinessAcquisitionAxis
= rbc_PTSMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember
Line of Credit [Member] | Term Facility [Member] | Subsequent Event [Member]                        
Debt Instrument, Term                       5 years
New Credit Facility                       $ 1,250,000,000us-gaap_LineOfCredit
/ us-gaap_DebtInstrumentAxis
= rbc_TermFacilityMember
/ us-gaap_LongtermDebtTypeAxis
= us-gaap_LineOfCreditMember
/ us-gaap_SubsequentEventTypeAxis
= us-gaap_SubsequentEventMember