Short- and Long-Term Obligations - Additional Information (Details) (USD $)	12 Months Ended
Jan. 03, 2015	Dec. 28, 2013
Debt Instrument [Line Items]
Weighted average interest rate for long-term obligations (in hundredths)	2.38%	2.74%
Unamortized debt issuance costs	$ 523,000us-gaap_UnamortizedDebtIssuanceExpense
Revolving credit facility
Debt Instrument [Line Items]
Terms of debt agreements	5 years
Borrowing capacity available under committed portion	100,000,000
Additional borrowing capacity	50,000,000
Maturity date	Nov. 01, 2018
Maximum amount of unrestricted U.S. cash	25,000,000
Maximum consolidated leverage ratio	3.5
Minimum consolidated interest charge coverage ratio	3
Long-term debt	20,000,000
Remaining borrowing capacity	77,463,000
Revolving credit facility \| Federal funds rate
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	0.50%
Revolving credit facility \| Federal funds rate \| Minimum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	0.00%
Revolving credit facility \| Federal funds rate \| Maximum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	1.00%
Revolving credit facility \| Prime rate \| Minimum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	0.00%
Revolving credit facility \| Prime rate \| Maximum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	1.00%
Revolving credit facility \| Eurocurrency rate
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	0.50%
Revolving credit facility \| Eurocurrency rate \| Minimum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	0.00%
Revolving credit facility \| Eurocurrency rate \| Maximum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	1.00%
Revolving credit facility \| Eurocurrency rate two \| Minimum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	1.00%
Revolving credit facility \| Eurocurrency rate two \| Maximum
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	2.00%
Commercial real estate loan
Debt Instrument [Line Items]
Terms of debt agreements	10 years
Long-term debt	5,750,000
Face amount of debt instrument	10,000,000
Quarterly payment of principal	125,000
Amount due at maturity	$ 5,000,000
Commercial real estate loan \| Three month LIBOR
Debt Instrument [Line Items]
Margin rate of debt instrument (in hundredths)	0.75%

Amount of the total principal payments to be made at final maturity of debt.

No definition available.

Name:	kai_DebtInstrumentAmountDueAtMaturity
Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Applicable marginal rate of debt instrument basis spread.

+ References

No definition available.

+ Details

Name:	kai_DebtInstrumentBasisSpreadOnApplicableMarginRate
Namespace Prefix:	kai_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

The additional amount available over and above the maximum borrowing capacity under the credit facility.

+ References

No definition available.

+ Details

Name:	kai_LineOfCreditFacilityAdditionalBorrowingCapacity
Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The maximum amount of unrestricted U.S. cash that can be netted against total debt.

+ References

No definition available.

+ Details

Name:	kai_LineOfCreditFacilityMaximumUnrestrictedDomesticCash
Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The maximum consolidated leverage ratio under the negative covenants of the credit facility.

+ References

No definition available.

+ Details

Name:	kai_MaximumConsolidatedLeverageRatio
Namespace Prefix:	kai_
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Balance Type:	na
Period Type:	duration

- Definition

The minimum consolidated interest charge coverage ratio (calculated as income before interest and taxes, divided by interest) to be in compliance with the financial covenant under an existing debt agreement.

+ References

No definition available.

+ Details

Name:	kai_MinimumConsolidatedInterestChargeCoverageRatio
Namespace Prefix:	kai_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

The term of the unsecured revolving credit facility agreement and commercial real estate loan.

+ References

No definition available.

+ Details

Name:	kai_PeriodOfDebtAgreements
Namespace Prefix:	kai_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 835

-SubTopic 30

-Section 45

-Paragraph 2

-URI http://asc.fasb.org/extlink&oid=6451184&loc=d3e28551-108399

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 835

-SubTopic 30

-Section 55

-Paragraph 8

-URI http://asc.fasb.org/extlink&oid=34725769&loc=d3e28878-108400

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_DebtInstrumentLineItems
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Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Date when the debt instrument is scheduled to be fully repaid, in CCYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 22

-Article 5

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 210

-SubTopic 10

-Section S99

-Paragraph 1

-Subparagraph (SX 210.5-02.22(a)(2))

-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of the required periodic payments applied to principal.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 210

-SubTopic 10

-Section S99

-Paragraph 1

-Subparagraph (SX 210.5-02.22)

-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 22

-Article 5

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of current borrowing capacity under the credit facility considering any current restrictions on the amount that could be borrowed (for example, borrowings may be limited by the amount of current assets), but without considering any amounts currently outstanding under the facility.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 210

-SubTopic 10

-Section S99

-Paragraph 1

-Subparagraph (SX 210.5-02.19(b),22(b))

-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 19, 22

-Article 5

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 210

-SubTopic 10

-Section S99

-Paragraph 1

-Subparagraph (SX 210.5-02.19(b),22(b))

-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 19, 22

-Article 5

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying amount of long-term debt, net of unamortized discount or premium, including current and noncurrent amounts. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 03

-Paragraph 16

-Article 7

Reference 2: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 210

-SubTopic 10

-Section S99

-Paragraph 1

-Subparagraph (SX 210.5-02.22)

-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 3: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 942

-SubTopic 210

-Section S99

-Paragraph 1

-Subparagraph (SX 210.9-03.16)

-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

Reference 4: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 03

-Paragraph 16

-Article 9

Reference 5: http://www.xbrl.org/2003/role/presentationRef

-Publisher SEC

-Name Regulation S-X (SX)

-Number 210

-Section 02

-Paragraph 20, 22

-Article 5

Reference 6: http://www.xbrl.org/2003/role/presentationRef

-Publisher FASB

-Name Accounting Standards Codification

-Topic 944

-SubTopic 210

-Section S99

-Paragraph 1

-Subparagraph (SX 210.7-03.16)

-URI http://asc.fasb.org/extlink&oid=6879938&loc=d3e572229-122910

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Weighted average interest rate of long-term debt outstanding.

+ References

No definition available.

+ Details

Name:	us-gaap_LongtermDebtWeightedAverageInterestRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The remaining balance of debt issuance expenses that were capitalized and are being amortized against income over the lives of the respective bond issues. This does not include the amounts capitalized as part of the cost of the utility plant or asset.

+ References

+ Details

Name:	us-gaap_UnamortizedDebtIssuanceExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_LongtermDebtTypeAxis=kai_CommercialRealEstateLoanMember
Namespace Prefix:
Data Type:	na
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Period Type:

- Details

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