Robot manipulator having a robot wrist with an offset

Claim 1

A robot manipulator comprising: an upper arm having a first end and a second end; a wrist coupled to said second end of said upper arm, said wrist including at least three rotational axes of articulation with one of said rotational axes offset from an intersection of another two of said rotational axes by a wrist offset; a first twist angle formed between a first of said at least three rotational axes and a second of said at least three rotational axes; a second twist angle formed between a third of said at least three rotational axes and said second rotational axis; a third twist angle formed between said second rotational axis and a line extending between said first end of said upper arm and an end of said wrist offset which is spaced from said second end of said upper arm; a distance between said first end of said upper arm and said wrist offset end which is spaced from said second end along said line is related to said first twist angle by the following (l 3 o ) 2 =(l 3 ) 2 +(d 5 ) 2 -2 * l 3 * d 5 * cos (180°-α 4 ) wherein l 3 o is said distance, l 3 is the length of said upper arm, d 5 is the length of said wrist offset and α 4 is said first twist angle; said third twist angle relates to said distance by the following ##EQU5## wherein l 4 o is said third angle; and said second angle is within the range of (2 * α.sub.4.sup.o -|α.sub.4 |)≦α.sub.5 ≦|α.sub.4 | wherein α 5 is said second twist angle.