Joseph Rodgers Wright was born in 1867, the son of Samuel Grayson Wright and Ann Elizabeth (nee Armitage).  He and his brothers became the third generation (at least) of table blade forgers, following in the footsteps of their father and grandfather (George Wright)

J. R. Wright married Mary Ann Lemons in 1888 and they went on to have 4 sons and 5 daughters. 
Joseph's second son, also called Joseph Rodgers Wright, was a teacher at Upperthorpe Boys School.  He enlisted as a Corporal in the Sheffield City Battalion (the "pals") and was killed at The Somme in 1916, aged 24.

Joseph describes himself in the 1911 census In Walkley as working "at home" for Maleham & Yeomans which indicates that he was producing blades in his own workshop under contract.  At some point, probably in the 1920s, he was making and selling stainless steel table knives under his own name.  On the 1921 census both he and his third son, Bernard, are working as table blade forgers for Thomas Turner & Co at their Suffolk Works so the J R Wright knives may have been a way to supplement the family income.

Joseph Rodgers Wright died on 24 March 1931, aged 64, and is buried in Walkley Cemetery with his wife (d.1946) and two of his sons. 

With thanks to Richard Jackson, a great-grandson of Joseph Rodgers Wright, for pointing us in the right direction.  He apparently owns a number of J R Wright knives.