The IGI has his parents as James and Elizabeth NIBB.
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In 1841, we see Richard living at Steventon, Berkshire, England with his wife Catherine:
Richard Knibbs Head 36
Catherine Knibbs Wife 30
Alfred Knibbs 10
Richard Knibbs 7(?)
John Knibbs 4(?)

We don't know for sure that Catherine's maiden surname was Goldsmith, but by tracking the movements of her sister, Charlotte HOWARD, who was living with her in 1851, we can see a definite link to the Goldsmith family in Canterbury.

In 1851, we see Catherine living at Chalvey, Eton, Buckinghamshire:
Catherine Knibbs Head Wid 41 Laundress Kent Canterbury
Richard Knibbs Son UnM 16 Grocers Boy Lancashire Manchester
John Knibbs Son 13 Scholar Middlesex Hounslow
Charlotte Howard Sister M 31 Kent Canterbury
Catherine Calvert Niece UnM 14 Kent Canterbury

Charlotte also appears in 1861, living with another siter of hers, Hannah Maria Oakenfull.
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In 1861, we see Catherine living at 2 Bridge Terrace, Paddington, London, Middlesex, England:
Catherine Knibbs Head Widow 50 Kent Canterbury
John Knibbs Son UnM 23 Railway Fireman Middlesex Hounslow
Emma M??? Servant UnM 16 Domestic Servant Middlesex Kensington
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In 1871 she was living at 20 Coruna Road, Battersea, London, Middlesex, England:
Catherine Knibbs Head Wid 65 No Occupation Kent Canterbury
John Knibbs UnM 33 Engine Driver Middlesex Hounslow

Her son Richard and his wife were living in the same household.
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In 1881, Catherine was living in the household of her son John at 41 Patmore Street, Battersea, Surrey, England:
John Knibbs Head UnM 43 Hounslow Middlesex Railway Engine Driver
Catherine Knibbs Mother Wid 73 Canterbury Kent
Alice Allen Tenant UnM 15 Brighton Sussex Domestic Servant