Debt And Bank Credit Facilities (Details On The Senior Notes) (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
Apr. 02, 2016	Jan. 02, 2016
Debt Instrument [Line Items]
Senior Notes		$ 600.0
Fixed Rate Series 2011A
Debt Instrument [Line Items]
Stated rate, minimum	4.80%
Stated rate, maximum	5.00%
Fixed Rate Series 2011A
Debt Instrument [Line Items]
Stated rate, minimum	4.90%
Stated rate, maximum	5.10%
Senior Notes
Debt Instrument [Line Items]
Senior Notes		$ 600.0
Senior Notes \| Floating Rate Series 2007A
Debt Instrument [Line Items]
Basis spread on variable rate	1.30%	1.10%
Senior Notes		$ 100.0
Senior Notes \| Fixed Rate Series 2011A
Debt Instrument [Line Items]
Senior Notes		$ 100.0
Debt instrument interest rate		4.10%
Senior Notes \| Fixed Rate Series 2011A
Debt Instrument [Line Items]
Senior Notes		$ 230.0
Senior Notes \| Fixed Rate Series 2011A
Debt Instrument [Line Items]
Senior Notes		$ 170.0

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

No definition available.

Name:	us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Maximum contractual interest rate for funds borrowed, under the debt agreement.

+ References

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentageRateRangeMaximum
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Minimum contractual interest rate for funds borrowed, under the debt agreement.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(2))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentageRateRangeMinimum
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Including the current and noncurrent portions, carrying value as of the balance sheet date of Notes with the highest claim on the assets of the issuer in case of bankruptcy or liquidation (with maturities initially due after one year or beyond the operating cycle if longer). Senior note holders are paid off in full before any payments are made to junior note holders.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03.16(a))
-URI http://asc.fasb.org/extlink&oid=6879938&loc=d3e572229-122910

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.16)
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

+ Details

Name:	us-gaap_SeniorNotes
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_DebtInstrumentAxis=rbc_FloatingRateSeriesTwoThousandElevenSeniorNotesMatureInJulyTwoThousandTwentyOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=rbc_FloatingRateSeriesTwoThousandElevenSeniorNotesMatureInJulyTwoThousandTwentyThreeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=rbc_FloatingRateSeriesTwoThousandSevenSeniorNotesMatureInAugustTwoThousandSeventeenMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=rbc_FloatingRateSeriesTwoThousandElevenSeniorNotesMatureInJulyTwoThousandEighteenMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: