A spherical orienting device includes a base, first and second actuation shafts, an orientable device, an inner member, a middle member, and an outer member. The first and second actuation shafts are rotatably held by the base for rotary actuation about first and second actuation axes, respectively, which intersect orthogonally at a spherical center of rotation. The orientable device is supported by first and second revolute support joints which are disposed for rotation about an orientation axis of the orientable device and a support axis, respectively. The inner member is fixed to the first actuation shaft and linked to the second support joint. The middle member is inwardly linked to the first support joint and outwardly linked to a middle revolute joint disposed for rotation about a linkage axis. The outer member is fixed to the second actuation shaft and linked to the middle revolute joint.