BUSINESS ACQUISITIONS (Narrative) (Details) - Angel's Instrumentation, Inc. [Member] - USD ($) $ in Millions	9 Months Ended
Dec. 29, 2018	Mar. 31, 2018
Business Acquisition [Line Items]
Business acquisition, consideration transferred	$ 4.7
Business acquisition, cash acquired	0.1
Business acquisition, contingent consideration unpaid	0.6
Business acquisition, other holdback amounts unpaid	0.5
Business acquisition, contingent consideration paid	$ 0.1
Maximum [Member]
Business Acquisition [Line Items]
Intangible assets acquired, useful life	10 years
Acquisition costs	$ 0.1

Business Combination, Other Amounts Unpaid, Current.

No definition available.

Name:	trns_BusinessCombinationOtherAmountsUnpaidCurrent
Namespace Prefix:	trns_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

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

- Definition

This element represents acquisition-related costs incurred to effect a business combination which costs have been expensed during the period. Such costs include finder's fees; advisory, legal, accounting, valuation, and other professional or consulting fees; general administrative costs, including the costs of maintaining an internal acquisitions department; and may include costs of registering and issuing debt and equity securities.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 25
-Paragraph 23
-URI http://asc.fasb.org/extlink&oid=84229725&loc=d3e1043-128460

+ Details

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

- Definition

Amount of consideration transferred, consisting of acquisition-date fair value of assets transferred by the acquirer, liabilities incurred by the acquirer, and equity interest issued by the acquirer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=109124213&loc=d3e6613-128477

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=35744584&loc=d3e6927-128479

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 30
-Paragraph 7
-URI http://asc.fasb.org/extlink&oid=109124213&loc=d3e6578-128477

+ Details

Name:	us-gaap_BusinessCombinationConsiderationTransferred1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of liability recognized arising from contingent consideration in a business combination.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (c)(1)
-URI http://asc.fasb.org/extlink&oid=35744584&loc=d3e6927-128479

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 35
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=6911338&loc=d3e6819-128478

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 25
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=6911189&loc=d3e6408-128476

+ Details

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

- Definition

Amount of liability recognized arising from contingent consideration in a business combination, expected to be settled within one year or the normal operating cycle, if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 25
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=6911189&loc=d3e6408-128476

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 30
-Section 35
-Paragraph 1
-Subparagraph b
-URI http://asc.fasb.org/extlink&oid=6911338&loc=d3e6819-128478

+ Details

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

- Definition

The cash inflow associated with the acquisition of business during the period (for example, cash that was held by the acquired business).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 12
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=109223946&loc=d3e3179-108585

+ Details

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

- Definition

Useful life of finite-lived intangible assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	us-gaap_FiniteLivedIntangibleAssetUsefulLife
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_BusinessAcquisitionAxis=trns_Fiscal2019AcquisitionsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: