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Shareholders' Equity (Details) (USD $)
In Thousands, except Share data, unless otherwise specified
3 Months Ended 9 Months Ended 12 Months Ended
Mar. 27, 2015
Mar. 28, 2014
Mar. 27, 2015
Mar. 28, 2014
Jun. 30, 2013
Jun. 30, 2012
Jul. 27, 2012
Feb. 01, 2008
Stockholders Equity [Line Items]                
Balance, beginning of period     $ 152,311us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest $ 143,562us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest        
Net income 3,047us-gaap_ProfitLoss (442)us-gaap_ProfitLoss 10,909us-gaap_ProfitLoss 1,488us-gaap_ProfitLoss        
Translation adjustments (5,892)us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax 1,054us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax (14,762)us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax 4,053us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax        
Benefit plan adjustments, net of tax 542us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax 528us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax 1,545us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax 1,506us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax        
Cash dividends     (3,266)us-gaap_DividendsCommonStockCash (3,532)us-gaap_DividendsCommonStockCash        
Compensation expense and windfall tax benefits     388twin_CompensationExpenseAndWindfallTaxBenefits 1,457twin_CompensationExpenseAndWindfallTaxBenefits        
Shares (acquired) issued, net     (298)twin_SharesAcquiredIssuedNet (2,169)twin_SharesAcquiredIssuedNet        
Balance, end of period 146,827us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest 146,365us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest 146,827us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest 146,365us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest        
Common Stock [Member]                
Stockholders Equity [Line Items]                
Number of shares authorize to repurchase (in shares)             375,000us-gaap_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
500,000us-gaap_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
Stock repurchased during period (in shares)         185,000us-gaap_StockRepurchasedDuringPeriodShares
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
125,000us-gaap_StockRepurchasedDuringPeriodShares
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
   
Balance, beginning of period     11,973us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
13,183us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
       
Compensation expense and windfall tax benefits     388twin_CompensationExpenseAndWindfallTaxBenefits
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
1,457twin_CompensationExpenseAndWindfallTaxBenefits
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
       
Shares (acquired) issued, net     (392)twin_SharesAcquiredIssuedNet
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
(2,964)twin_SharesAcquiredIssuedNet
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
       
Balance, end of period 11,969us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
11,676us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
11,969us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
11,676us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
13,183us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonStockMember
     
Retained Earnings [Member]                
Stockholders Equity [Line Items]                
Balance, beginning of period     183,695us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
184,110us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
       
Net income     10,736us-gaap_ProfitLoss
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
1,320us-gaap_ProfitLoss
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
       
Cash dividends     (3,047)us-gaap_DividendsCommonStockCash
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
(3,045)us-gaap_DividendsCommonStockCash
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
       
Balance, end of period 191,384us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
182,385us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
191,384us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
182,385us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_RetainedEarningsMember
       
Accumulated Other Comprehensive Income (Loss) [Member]                
Stockholders Equity [Line Items]                
Balance, beginning of period     (15,943)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
(25,899)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
       
Translation adjustments     (14,676)us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
4,137us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
       
Benefit plan adjustments, net of tax     1,545us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
1,506us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansNetOfTax
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
       
Balance, end of period (29,074)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
(20,256)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
(29,074)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
(20,256)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_AccumulatedOtherComprehensiveIncomeMember
       
Treasury Stock [Member]                
Stockholders Equity [Line Items]                
Balance, beginning of period     (28,141)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
(28,890)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
       
Shares (acquired) issued, net     94twin_SharesAcquiredIssuedNet
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
795twin_SharesAcquiredIssuedNet
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
       
Balance, end of period (28,047)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
(28,095)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
(28,047)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
(28,095)us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_TreasuryStockMember
       
Non-Controlling Interest [Member]                
Stockholders Equity [Line Items]                
Balance, beginning of period     727us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
1,058us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
       
Net income     173us-gaap_ProfitLoss
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
168us-gaap_ProfitLoss
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
       
Translation adjustments     (86)us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
(84)us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
       
Cash dividends     (219)us-gaap_DividendsCommonStockCash
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
(487)us-gaap_DividendsCommonStockCash
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
       
Balance, end of period $ 595us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
$ 655us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
$ 595us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember
$ 655us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_NoncontrollingInterestMember