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Income Taxes - Additional Information (Details) (USD $)
 12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Operating Loss Carryforwards [Line Items]      
Deferred tax assets, Valuation allowance $ 13,040,000us-gaap_DeferredTaxAssetsValuationAllowance $ 13,905,000us-gaap_DeferredTaxAssetsValuationAllowance  
Increase (decrease) of deferred tax asset valuation allowance (865,000)us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount    
Undistributed earings of foreign subsidiaries 169,178,000us-gaap_UndistributedEarningsOfForeignSubsidiaries    
Estimated withholding liability related to undistributed earnings of foreign subsidiaries 2,972,000kai_EstimatedWithholdingLiabilityRelatedToUndistributedEarningsOfForeignSubsidiaries    
Unrecognized tax benefits that would impact effective tax rate 5,006,000us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate    
Income tax penalties and accrued interest from unrecognized tax benefits 1,137,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued 1,776,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued  
Income tax penalties and interest (benefit) expense from unrecognized tax benefits (648,000)us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense 205,000us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense  
Upper bound estimated range of change of significant (increase) decrease in unrecognized tax benefits 770,000us-gaap_SignificantChangeInUnrecognizedTaxBenefitsIsReasonablyPossibleEstimatedRangeOfChangeUpperBound    
Tax benefits related to employees' and directors' stock plans 771,000us-gaap_AdjustmentsToAdditionalPaidInCapitalTaxEffectFromShareBasedCompensation 351,000us-gaap_AdjustmentsToAdditionalPaidInCapitalTaxEffectFromShareBasedCompensation 132,000us-gaap_AdjustmentsToAdditionalPaidInCapitalTaxEffectFromShareBasedCompensation
Percent of effective income tax rate reconciliation at the federal statutory income tax rate 35.00%us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate    
Estimate time frame for significant change in unrecognized tax benefits 12 months    
Internal revenue service (IRS)      
Operating Loss Carryforwards [Line Items]      
Deferred tax assets, Valuation allowance 1,401,000us-gaap_DeferredTaxAssetsValuationAllowance
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_InternalRevenueServiceIRSMember		    
Foreign tax authority      
Operating Loss Carryforwards [Line Items]      
Deferred tax assets, Valuation allowance 11,639,000us-gaap_DeferredTaxAssetsValuationAllowance
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember		    
Operating loss carryforwards 42,182,000us-gaap_OperatingLossCarryforwards
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember		    
Operating loss carryforwards expiring in 2017 through 2023 195,000kai_OperatingLossCarryforwardsExpiringin2017Through2023
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_ForeignCountryMember		    
State and local jurisdiction      
Operating Loss Carryforwards [Line Items]      
Operating loss carryforwards 30,290,000us-gaap_OperatingLossCarryforwards
/ us-gaap_IncomeTaxAuthorityAxis
= us-gaap_StateAndLocalJurisdictionMember		    
Alternative minimum tax credit      
Operating Loss Carryforwards [Line Items]      
Tax credit carryfoward amount $ 697,000us-gaap_TaxCreditCarryforwardAmount
/ us-gaap_TaxCreditCarryforwardAxis
= kai_AlternativeMinimumTaxCreditMember