Debt And Bank Credit Facilities (Maturities Of Long-Term Debt) (Details) (USD $) In Millions, unless otherwise specified	12 Months Ended
Jan. 03, 2015	Dec. 28, 2013
Debt Instrument [Line Items]
Senior Notes	$ 600.0us-gaap_SeniorNotes	$ 750.0us-gaap_SeniorNotes
2015	8.4
2016	17.5
2017	103.3
2018	100.5
2019	0.5
Thereafter	403.6
Long-term debt, Total	633.8us-gaap_LongTermDebt	767.4us-gaap_LongTermDebt
Notes Payable	600.0us-gaap_NotesPayable
Floating Rate Series Two Thousand Seven Senior Notes Mature In August Two Thousand Seventeen [Member]
Debt Instrument [Line Items]
Senior Notes	100.0
Debt Instrument, Interest Rate Terms	Floating (1)
Debt Instrument, Maturity Date	Aug. 01, 2017
Fixed Rate Series 2011A Mature In July 2018 [Member]
Debt Instrument [Line Items]
Senior Notes	100.0
Debt Instrument, Interest Rate, Stated Percentage	4.10%
Debt Instrument, Maturity Date	Jul. 01, 2018
Floating Rate Series Two Thousand Eleven Senior Notes Mature In July Two Thousand Twenty One [Member]
Debt Instrument [Line Items]
Debt Instrument, Interest Rate, Stated Percentage Rate Range, Minimum	4.80%
Debt Instrument, Interest Rate, Stated Percentage Rate Range, Maximum	5.00%
Senior Notes	230.0
Debt Instrument, Maturity Date	Jul. 01, 2021
Floating Rate Series Two Thousand Eleven Senior Notes Mature In July Two Thousand Twenty Three [Member]
Debt Instrument [Line Items]
Debt Instrument, Interest Rate, Stated Percentage Rate Range, Minimum	4.90%
Debt Instrument, Interest Rate, Stated Percentage Rate Range, Maximum	5.10%
Senior Notes	$ 170.0
Debt Instrument, Maturity Date	Jul. 01, 2023

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

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 22

-Article 5

Reference 2: 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 SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 22

-Article 5

Reference 2: 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

Description of the interest rate as being fixed or variable, and, if variable, identification of the index or rate on which the interest rate is based and the number of points or percentage added to that index or rate to set the rate, and other pertinent information, such as frequency of rate resets.

+ References

+ Details

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

- Details

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

- Definition

Date when the debt instrument is scheduled to be fully repaid, in CCYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 22

-Article 5

Reference 2: 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_DebtInstrumentMaturityDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Carrying amount of long-term debt, net of unamortized discount or premium, including current and noncurrent amounts. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 03

-Paragraph 16

-Article 7

Reference 2: 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)

-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 3: 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

Reference 4: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 03

-Paragraph 16

-Article 9

Reference 5: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 20, 22

-Article 5

Reference 6: 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)

-URI http://asc.fasb.org/extlink&oid=6879938&loc=d3e572229-122910

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirements, and other securities issued that are redeemable by holder at fixed or determinable prices and dates maturing after the fifth fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 470

-SubTopic 10

-Section 50

-Paragraph 1

-URI http://asc.fasb.org/extlink&oid=6802200&loc=d3e1835-112601

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 235

-SubTopic 10

-Section S99

-Paragraph 3

-Subparagraph (SX 210.12-04.(a))

-URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e24072-122690

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirements, and other securities issued that are redeemable by holder at fixed or determinable prices and dates maturing in the next fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date.

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirements, and other securities issued that are redeemable by holder at fixed or determinable prices and dates maturing in the fifth fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date.

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirements, and other securities issued that are redeemable by holder at fixed or determinable prices and dates maturing in the fourth fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date.

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirements, and other securities issued that are redeemable by holder at fixed or determinable prices and dates maturing in the third fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date.

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirements, and other securities issued that are redeemable by holder at fixed or determinable prices and dates maturing in the second fiscal year following the latest fiscal year. Excludes interim and annual periods when interim periods are reported on a rolling approach, from latest balance sheet date.

+ References

+ Details

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

- Definition

Including the current and noncurrent portions, aggregate carrying amount of all types of notes payable, as of the balance sheet date, with initial maturities beyond one year or beyond the normal operating cycle, if longer.

+ References

Reference 1: 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

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 19, 20, 22

-Article 5

Reference 3: 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)

-URI http://asc.fasb.org/extlink&oid=6879938&loc=d3e572229-122910

Reference 4: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 03

-Paragraph 13, 16

-Article 9

+ Details

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

- 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 942

-SubTopic 210

-Section S99

-Paragraph 1

-Subparagraph (SX 210.9-03.16)

-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

Reference 2: 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 3: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 03

-Paragraph 16

-Article 9

+ Details

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

- Details

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

- Details

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

- Details

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

- Details

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