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

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- Definition Amount of increase in additional paid in capital (APIC) resulting from a tax benefit associated with share-based compensation plan other than an employee stock ownership plan (ESOP). Includes, but is not limited to, excess tax benefit. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 505 -SubTopic 10 -Section 50 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=6928386&loc=d3e21463-112644 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 505 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.3-04) -URI http://asc.fasb.org/extlink&oid=27012166&loc=d3e187085-122770 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 740 -Section 45 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=6419406&loc=d3e23524-113945 + Details
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- Definition Amount of (increase) decrease reasonably possible in the estimated upper bound of the unrecognized tax benefit for a tax position taken or expected to be taken. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15 -Subparagraph (d) -URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32718-109319 + Details
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- Definition Amount accrued for interest on an underpayment of income taxes and penalties related to a tax position claimed or expected to be claimed in the tax return. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15 -Subparagraph (c) -URI http://asc.fasb.org/extlink&oid=6907707&loc=d3e32718-109319 + Details
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