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Summary of Significant Accounting Policies (Narrative) (Details) (USD $)
 3 Months Ended 12 Months Ended
Dec. 29, 2013
Dec. 28, 2014
Dec. 29, 2013
Dec. 30, 2012
Jan. 01, 2012
Contingent shares under compensation plan   0tdy_ContingentSharesUnderCompensationPlan 0tdy_ContingentSharesUnderCompensationPlan 0tdy_ContingentSharesUnderCompensationPlan  
Fiscal Year          
Fiscal period, length   364 days 364 days 364 days  
Research and Development          
Selling, general and administrative expenses include company-funded research and development   $ 166,900,000tdy_SellingGeneralAndAdministrativeExpensesIncludeCompanyFundedResearchAndDevelopment $ 167,000,000tdy_SellingGeneralAndAdministrativeExpensesIncludeCompanyFundedResearchAndDevelopment $ 131,600,000tdy_SellingGeneralAndAdministrativeExpensesIncludeCompanyFundedResearchAndDevelopment  
Costs related to customer-funded research and development contracts   261,900,000tdy_CostsRelatedToCustomerFundedResearchAndDevelopmentContracts 221,200,000tdy_CostsRelatedToCustomerFundedResearchAndDevelopmentContracts 232,600,000tdy_CostsRelatedToCustomerFundedResearchAndDevelopmentContracts  
Income Tax Disclosure          
Number of years of cumulative operating income used to determine income tax valuation allowance   3 years      
Accounts Receivable          
Reserve for doubtful accounts 5,200,000us-gaap_AllowanceForDoubtfulAccountsReceivable 7,800,000us-gaap_AllowanceForDoubtfulAccountsReceivable 5,200,000us-gaap_AllowanceForDoubtfulAccountsReceivable    
Expense of reserve for doubtful accounts   3,600,000tdy_ExpenseOfReserveForDoubtfulAccounts 900,000tdy_ExpenseOfReserveForDoubtfulAccounts 700,000tdy_ExpenseOfReserveForDoubtfulAccounts  
Cash and Cash Equivalents          
Cash and cash equivalents 66,000,000us-gaap_CashAndCashEquivalentsAtCarryingValue 141,400,000us-gaap_CashAndCashEquivalentsAtCarryingValue 66,000,000us-gaap_CashAndCashEquivalentsAtCarryingValue 45,800,000us-gaap_CashAndCashEquivalentsAtCarryingValue 49,400,000us-gaap_CashAndCashEquivalentsAtCarryingValue
Cash held in foreign bank accounts   118,700,000tdy_CashEquivalentsatCarryingValueHeldinForeignBankAccounts      
Maximum maturity of money market mutual funds and bank deposits   3 months      
Capital expenditures          
Depreciation expense on property, plant and equipment, including assets under capital leases   62,300,000us-gaap_Depreciation 59,600,000us-gaap_Depreciation 48,900,000us-gaap_Depreciation  
Goodwill and Other Intangible Assets          
Impairment of intangible assets 1,200,000us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill 700,000us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill      
Impairment of goodwill   0us-gaap_GoodwillImpairmentLoss 0us-gaap_GoodwillImpairmentLoss    
Supplemental Cash Flow Information          
Cash payments for federal, foreign and state income taxes   75,000,000tdy_CashPaymentsForFederalForeignAndStateIncomeTaxes 32,800,000tdy_CashPaymentsForFederalForeignAndStateIncomeTaxes 15,000,000tdy_CashPaymentsForFederalForeignAndStateIncomeTaxes  
Tax refunds received totaled   2,300,000us-gaap_ProceedsFromIncomeTaxRefunds 3,300,000us-gaap_ProceedsFromIncomeTaxRefunds 1,900,000us-gaap_ProceedsFromIncomeTaxRefunds  
Cash payments for interest and credit facility fees totaled   17,600,000tdy_CashPaymentsForInterestAndCreditFacilityFees 19,700,000tdy_CashPaymentsForInterestAndCreditFacilityFees 16,200,000tdy_CashPaymentsForInterestAndCreditFacilityFees  
Minimum          
Fiscal Year          
Fiscal period, length   364 days      
Minimum | Equipment          
Capital expenditures          
Property, plant and equipment, useful life   5 years      
Minimum | Computer Hardware and Software          
Capital expenditures          
Property, plant and equipment, useful life   3 years      
Maximum          
Fiscal Year          
Fiscal period, length   371 days      
Maximum | Buildings          
Capital expenditures          
Property, plant and equipment, useful life   45 years      
Maximum | Equipment          
Capital expenditures          
Property, plant and equipment, useful life   18 years      
Maximum | Computer Hardware and Software          
Capital expenditures          
Property, plant and equipment, useful life   7 years      
Money market funds          
Cash and Cash Equivalents          
Cash equivalents $ 300,000us-gaap_CashEquivalentsAtCarryingValue
/ us-gaap_CashAndCashEquivalentsAxis
= us-gaap_MoneyMarketFundsMember		 $ 0us-gaap_CashEquivalentsAtCarryingValue
/ us-gaap_CashAndCashEquivalentsAxis
= us-gaap_MoneyMarketFundsMember		 $ 300,000us-gaap_CashEquivalentsAtCarryingValue
/ us-gaap_CashAndCashEquivalentsAxis
= us-gaap_MoneyMarketFundsMember