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Stock-Based Compensation (Details) (USD $)
3 Months Ended 9 Months Ended
Mar. 27, 2015
Mar. 28, 2014
Mar. 27, 2015
Mar. 28, 2014
Jun. 30, 2014
Performance Stock Unit Awards [Member]          
Schedule of Share Based Compensation Arrangements by Options Activity and Exercise Price Range [Line Items]          
Stock awards granted (in shares)     15,861us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
43,154us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
 
Stock awards vesting period     3 years 3 years  
Number of shares of common stock that can be granted, maximum (in shares) 13,621us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
22,205us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
13,621us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
22,205us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
 
Unvested stock awards outstanding (in shares) 48,594us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
54,874us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
48,594us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
54,874us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
 
Compensation cost, recognized $ 0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
$ 0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
$ 0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
$ 0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
 
Weighted average grant date fair value of unvested awards (in dollars per share) $ 24.70us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
  $ 24.70us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Total fair value of stock awards vested     0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
 
Accrued liabilities, employee benefits 0us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
  0us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
  0us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
Unrecognized compensation expense related to unvested shares 847,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
  847,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Performance Stock Awards [Member]          
Schedule of Share Based Compensation Arrangements by Options Activity and Exercise Price Range [Line Items]          
Stock awards granted (in shares)     16,261us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
17,312us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
 
Stock awards vesting period     3 years 3 years  
Number of shares of common stock that can be granted, maximum (in shares) 14,101us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
17,038us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
14,101us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
17,038us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
 
Unvested stock awards outstanding (in shares) 51,478us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
59,453us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
51,478us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
59,453us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
 
Compensation cost, recognized 0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
0us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
 
Weighted average grant date fair value of unvested awards (in dollars per share) $ 24.04us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
  $ 24.04us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
   
Total fair value of stock awards vested     0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
 
Unrecognized compensation expense related to unvested shares 1,238,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
  1,238,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= twin_PerformanceStockAwardsMember
   
Restricted Stock [Member]          
Schedule of Share Based Compensation Arrangements by Options Activity and Exercise Price Range [Line Items]          
Stock awards granted (in shares)     57,216us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
51,004us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Unvested stock awards outstanding (in shares) 97,789us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
119,297us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
97,789us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
119,297us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Compensation cost, recognized 8,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
308,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
425,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
934,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Total fair value of stock awards vested     941,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
3,053,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Unrecognized compensation expense related to unvested shares $ 1,227,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
  $ 1,227,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Recognition period for unrecognized compensation expense     3 years    
Restricted Stock [Member] | Minimum [Member]          
Schedule of Share Based Compensation Arrangements by Options Activity and Exercise Price Range [Line Items]          
Stock awards vesting period     1 year    
Restricted Stock [Member] | Maximum [Member]          
Schedule of Share Based Compensation Arrangements by Options Activity and Exercise Price Range [Line Items]          
Stock awards vesting period     4 years