Retirement Plans (Level 3 Plan Assets) (Details) - USD ($) $ in Millions	12 Months Ended
Dec. 31, 2022	Jan. 01, 2022
Change in Fair Value of Plan Assets:
Fair Value of Plan Assets at Beginning of Period	$ 478.9
Fair Value of Plan Assets at End of Period	346.2	$ 478.9
Level 3
Change in Fair Value of Plan Assets:
Fair Value of Plan Assets at Beginning of Period	34.0	10.0
Acquisition	0.0	33.6
Net Sales	(0.2)	(11.6)
Net (Losses) Gains	(10.7)	3.0
Translation	(2.2)	(1.0)
Fair Value of Plan Assets at End of Period	20.9	34.0
Level 3 \| Real Estate Fund
Change in Fair Value of Plan Assets:
Fair Value of Plan Assets at Beginning of Period	0.0	10.0
Acquisition		0.0
Net Sales		(11.6)
Net (Losses) Gains		1.6
Translation		0.0
Fair Value of Plan Assets at End of Period		0.0
Level 3 \| Insurance Contracts
Change in Fair Value of Plan Assets:
Fair Value of Plan Assets at Beginning of Period	34.0	0.0
Acquisition	0.0	33.6
Net Sales	(0.2)	0.0
Net (Losses) Gains	(10.7)	1.4
Translation	(2.2)	(1.0)
Fair Value of Plan Assets at End of Period	$ 20.9	$ 34.0

Amount, measured using unobservable inputs, of increase (decrease) in plan assets of defined benefit plan from actual return (loss) on assets still held.

Name:	us-gaap_DefinedBenefitPlanActualReturnOnPlanAssetsStillHeld
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount, measured using unobservable inputs, of increase (decrease) in plan assets of defined benefit plan.

+ References

No definition available.

+ Details

Name:	us-gaap_DefinedBenefitPlanChangeInFairValueOfPlanAssetsLevel3ReconciliationPeriodIncreaseDecrease
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	duration

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Amount of asset segregated and restricted to provide benefit under defined benefit plan. Asset includes, but is not limited to, stock, bond, other investment, earning from investment, and contribution by employer and employee.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (d)(iv)(01)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (d)(iv)(01)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (d)(ii)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 55
-Paragraph 17
-URI https://asc.fasb.org/extlink&oid=123450688&loc=d3e4179-114921

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (d)(iv)(02)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

Reference 7: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (d)(ii)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

+ Details

Name:	us-gaap_DefinedBenefitPlanFairValueOfPlanAssets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, measured using unobservable input, of decrease in plan asset of defined benefit plan from sale.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 715
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (d)(iv)(02)(B)
-URI https://asc.fasb.org/extlink&oid=123447040&loc=d3e1928-114920

+ Details

Name:	us-gaap_DefinedBenefitPlanPlanAssetsLevel3ReconciliationDecreaseForSale
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount, measured using unobservable input, of increase in plan asset of defined benefit plan from purchase.

+ References

+ Details

Name:	us-gaap_DefinedBenefitPlanPlanAssetsLevel3ReconciliationIncreaseForPurchase
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel3Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis=us-gaap_RealEstateInvestmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DefinedBenefitPlanByPlanAssetCategoriesAxis=rbc_InsuranceContractsPlanAssetsCategoryMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: