He taught in Rhode Island public schools for four years, then obtained a master's degree and doctorate at the University of Massachusetts, Amherst. He studied philosophy and wrote his dissertation on French philosopher and scientist Rene Descartes.
He met his future wife, Patricia "Pat" Farrell, when both were Brown University students.
He became a University of Massachusetts administrator and assisted students enrolled in special programs, such as University Without Walls and the Women's Equity Project.
"He could figure out ways to work in a complex bureaucracy," said his wife, who is a certified public accountant. "He helped students navigate how to make the school's idiosyncratic programs work.
"His style was quiet and understated," she said. "He was a good listener. He thought it was important that people express opinions."
In 1985 he was named dean of Homewood schools administration at the Johns Hopkins University, working in admissions, financial aid and student life. He moved to Calvert Street in Charles Village and became a community activist.
In 1989, he became Goucher College's associate dean and later dean of academic affairs.
A 1999 Baltimore Sun article said of the school: "Even the value of the time-tested liberal arts education is questioned by prospective students who are increasingly vocationally oriented, seeking the kind of applied, practical and technical programs that lead directly to employment."
"Many of our applicants, and more often their parents, say to me, 'What can I do with this degree?'" said Dr. Welch in the article. "I tell them, 'Just about anything you want to.'"
Goucher's trustees named Dr. Welch its acting president for the 2000-2001 school year.
"He was instrumental in expanding the college's program of continuing education, and the Robert S. Welch Center for Graduate and Professional Studies was named in his honor," said a Goucher colleague, John Rose.
"Bob had all the true academic sensibilities but did not come up through the traditional faculty ranks," said former Goucher president Judy Jolley Mohraz of Phoenix, Ariz. "He was a remarkable administrator and a problem solver who used his analytical skills from his philosophy training to think through challenges the college faced."
After Goucher president Sanford J. Ungar was inaugurated in 2001, Dr. Welch returned to the classroom to teach philosophy.
"After many years he got to be a classroom teacher," his wife said. "He did his career entirely backward, but it was OK."
Dr. Rose, his friend and a philosophy professor, said: "Bob always expressed his joy that he had come over from the 'dark side,' as he put it, to do the teaching that the college was really about. He devoted his life to serving students to think, write and speak with clarity and distinctness.
"Bob was a true servant to Goucher who always held the good of the students, the faculty, and the college foremost in his mind," Dr. Rose said. "He was a leader who led from behind, and created room for discussion and deliberation with those with whom he worked. He offered multiple solutions when approaching a situation and allowed his colleagues to choose the best path for them."
He retired in 2014.
Dr. Welch was also a skilled home beer brewer who devoted many years to his hobby.
"He really knew his beer," said a Charles Village neighbor, Judge Edward R.K. Hargadon of the Circuit Court for Baltimore City. "He was a beer aficionado and many of us sat at his knee and learned.
"He was an integral part of a 1990s effort to rejuvenate the neighborhood," Judge Hargadon said. "He was integral in the beginning of the Charles Village festival and worked tirelessly to make it a success. He ran the beer sales and probably brought in half the festival's revenues. He knew everybody and had a way of schmoozing tavern owners and liquor stores for donations."