Believe I have found him. He appears to have arrived in the US 4 years later than he said - on Castle Garden site I found:
Richard Robinson (born Scotland) 23 Iron Worker arrived on 'Victoria' 23/9/1874.
I note he married Lizzie Scott 26/1/1882 Kings, New York.
Could find no birth/baptism entry for Richard in Scotland so looked at census.
1871 - shown bc.1851 Scotland and a boarder in Benfieldside, Durham, England - occup.Puddler (in manufacture of iron)
1861 - same place he is a 9yr old schoolboy with brother Robert Robinson 21 Puddler born Ireland
(cannot find rest of his family)
1851 - 55 South Square, Old Monkland, Lanarkshire
Ann Robinson widow 38 born Ireland
James Robinson 13 ditto
Robert Robinson 12 ditto
John Robinson 9 born Old Monkland, Lanarkshire
Dorinda Robinson 7 ditto
Andrew Robinson 5 ditto
Ann J. Robinson 2 ditto
William McFadyn 30 boarder Puddler of Iron born Ireland
Dorinda McFadyn 35 ditto
One of the US census I looked at gave Richard's birthdate as June 1851 so mother Ann was about to give birth to him.
I then found some trees online (some of whom I could see had some incorrect information) and a synopsis seems to be:
Parents were James Robinson bc.1810 Scotland d.end 1850/early 1851. When his daughter Dorinda married (to Isaiah Hughes) 12/8/1864 at Baptist Chapel of Highgate, Durham she states father James, deceased - he married Ann Jane Baird Farrall (or Farrell) presumably in Ireland as she and first 2 children born there. Ann died 16/4/1859 Old Monkland, Lanarkshire - she was shown as widow of Blast Furnaceman (his name not given on death certificate which I viewed on Scotlands People). She died of Peritonitis and shown to be the daughter of Andrew Farrall, farmer and Margaret McNee ??(hard to read). (Civil registration didn't start in Scotland until 1855 so unable to view James' death details). Informant of her death was son John.
Haven't followed all Richard's siblings but trees show Dorinda died 28/5/1924 Detroit, Michigan and sister Ann Jane married an Atchison Scott 5/9/1872 in USA, and died 1932 New Jersey. So clearly, some of his siblings did go to the US too but he arrived on his own.
There is a photo of his sister Dorinda on some of the trees I looked at. (Trees said father James died 1854 but his wife shown as a widow on 1851 census, and that Ann died 1858 in Preston, Lancs. England which is definitely wrong as she died in Scotland the following year).
As I said at the outset, there is no birth/baptism entry for Richard either on familysearch or SP, nor indeed for any of his siblings born in Scotland. He did in fact have 4 brothers and 2 sisters.
Annette