Born on 8 July 1770, he was, like his father John Machin, a master potter and also a Methodist. When his father died in 1789, his will departed from the norm by leaving his, business interests, workshops, houses and land to his fifth wife Elizabeth rather that to any or all of his three sons. When she died in 1800 she left everything to her youngest son, Joseph. By 1793 Joseph Machin is listed as an Enameller of Burslem. Shortly after taking over the family firm Joseph developed the scope of the business. In 1829 Simeon Shaw wrote that in Burslem the next largest manufacturer to Enoch Wood was Josh. Machin & Co., adding that Joseph was a Steward and principal supporter of the Wesleyan Methodist Society in Burslem. When Joseph died the business was taken over by his son William (1804-1874) who extended its scope by introducing new inventions and products, such as busts of Adam Clarke in October 1832 and of John Wesley in readiness for the1839 Centenary.
Machin was a Steward and benefactor of Swan Bank Wesleyan Church, Burslem. His life was scarred by many tragedies. He married Ann Wood, the daughter of Aaron Wood, in 1794; she died in 1801. Then he married Ann's cousin Abigail Wood, the mother of William and of Thomas, who was deaf and dumb from birth. She died in 1808. A year later he married Jane Tomlinson of Chester. She died in 1816. Two years later Joseph married Ann Dean of Chester, who died in 1820. On a visit to the Bourne family in Derbyshire he met Mary Bourne, a widow of 16 years whom he married 1823. Joseph himself suffered a long and painful illness, but through all these tragedies his strong faith never wavered. He was a life-long Wesleyan and a Steward and benefactor of Swan Bank Wesleyan Church, Burslem. Along with Enoch Wood he was a committee member of the non-denominational Burslem Sunday School, which met on the Swan Bank premises and was an outstanding project in the education of the unschooled children of the town. Joseph made generous donations to the Swan Bank extension funds. In 1816 he signed a letter to the President of the Conference on behalf of the Trustees and Leaders, asking the Conference to grant Swan Bank the privilege of having the Sacrament administered by their preachers. He died on 7 July 1831.
On display at the Epworth Old Rectory is a plate which is inscribed 'Presented to the Revd Jn. Bryan for the use of the Methodist Congregation at Epworth by Joseph Machin of Burslem, Staffordshire 1823'.