In this paper we present a method for recognising three fundamental movements of the human arm (reach and retrieve, lift cup to mouth, rotation of the arm) by determining the orientation of a tri-axial accelerometer located near the wrist. Our objective is to detect the occurrence of such movements performed with the impaired arm of a stroke patient during normal daily activities as a means to assess their rehabilitation. The method relies on accurately mapping transitions of predefined, standard orientations of the accelerometer to corresponding elementary arm movements. To evaluate the technique, kinematic data was collected from four healthy subjects and four stroke patients as they performed a number of activities involved in a representative activity of daily living, 'making-a-cup-of-tea'. Our experimental results show that the proposed method can independently recognise all three of the elementary upper limb movements investigated with accuracies in the range 91-99% for healthy subjects and 70-85% for stroke patients.