What are the design or selection criteria for robots that will be capable of carrying out particular functions? How can robots and machines be installed in work locations to obtain maximum effectiveness? How can their programming be made easier? How can a work location be arranged so as to accommodate successfully automatic machines? Traditionally, these questions have only been answered as a result of long and exhaustive study, involving complex calculations and the use of many sketches and plans. Computers and interactive computer graphics provide the possibility of automation for this type of analysis, thus making the task of robot designers and users easier. This volume is concerned with mathematical modelling and graphics representation of robot performance (eg their fields of action, their performance index) as a function of their structure, mechanical parts and memory systems. Used in conjunction with operating specifications, such as movement programs and computer-aided design (CAD) data bases that describe parts or tools, these perform­ ance models can allow the potential of different robots or different models of the same type of robot to be compared, workstations to be organized efficiently, responses to be optimized, errors to be minimized and can make off-line programming by computer a real possibility. In the future, it is certain that the appearance of robots designed to monitor their own performances will allow applications and safety conditions to be considerably improved.