Income Taxes (Statutory Tax Rate and Effective Tax Rate) (Details)	12 Months Ended
Jan. 02, 2021	Dec. 28, 2019	Dec. 29, 2018
Income Taxes [Line Items]
Federal Statutory Rate	21.00%	21.00%	21.00%
State Income Taxes, Net of Federal Benefit	0.80%	1.30%	1.10%
Research and Development Credit	(3.00%)	(2.50%)	(2.50%)
Valuation Allowance	(0.10%)	0.80%	(0.30%)
Tax Cuts and Jobs Act of 2017	0	0	(0.013)
Tax on Repatriation	1.20%	3.40%	1.30%
Adjustments to Tax Accruals and Reserves	0.10%	0.30%	0.00%
Tax Impact of Divestitures	0.00%	(1.70%)	0.00%
Other	1.90%	(0.60%)	0.50%
Effective Tax Rate	22.70%	20.10%	19.30%
China
Income Taxes [Line Items]
Foreign Rate Differential	1.20%	0.90%	0.90%
All Other Tax Authorities
Income Taxes [Line Items]
Foreign Rate Differential	(0.40%)	(2.80%)	(1.40%)

Effective Income Tax Rate Reconciliation, Adjustments To Tax Accruals And Reserves, Percent

No definition available.

Name:	rbc_EffectiveIncomeTaxRateReconciliationAdjustmentsToTaxAccrualsAndReservesPercent
Namespace Prefix:	rbc_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

[Line Items] for Income Taxes [Table]

+ References

No definition available.

+ Details

Name:	rbc_IncomeTaxesLineItems
Namespace Prefix:	rbc_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

+ Details

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

- Definition

Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

+ Details

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

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to changes in the valuation allowance for deferred tax assets.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

+ Details

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

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to disposition of a business not qualifying as a discontinued operation.

+ References

+ Details

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

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to statutory income tax expense (benefit) outside of the country of domicile.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

+ Details

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

- Definition

+ References

+ Details

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

- Definition

+ References

+ Details

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

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to state and local income tax expense (benefit), net of federal tax expense (benefit).

+ References

+ Details

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

- Definition

+ References

+ Details

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

- Definition

Percentage of reported income tax expense (benefit) in excess of (less than) expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operations, attributable to Tax Cuts and Jobs Act.

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationTaxCutsAndJobsActOf2017Percent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_IncomeTaxAuthorityAxis=country_CN
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeTaxAuthorityAxis=rbc_AllOtherTaxAuthoritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: