A link operating device comprising: a proximal-end-side link hub; a distal-end-side link hub; at least three link mechanisms via which the distal-end-side link hub is connected to the proximal-end-side link hub so as to be changeable in position relative thereto, each link mechanism including a proximal-side end link member having one end pivotably coupled to the proximal-end-side link hub, a distal-side end link member having one end pivotably coupled to the distal-end-side link hub, and a center link member having opposite ends pivotably coupled to the other end of the proximal-side end link member and the other end of the distal-side end link member, respectively; position-controlling actuators provided to two or more link mechanisms among the at least three link mechanisms, and each configured to arbitrarily change a position of the distal-end-side link hub relative to the proximal-end-side link hub; and speed reduction mechanisms each configured to reduce a speed of rotation and transmit a rotational power to the corresponding proximal-side end link member, wherein the proximal-side end link member includes a bent portion bent at an arbitrary angle, and a rotational connection portion (31A, 31B) disposed at one end of the bent portion and including a pair of rotational connection bodies (31a, 31b) arranged so as to be spaced from each other, each speed reduction mechanism includes an input shaft and an output shaft coaxial with each other, and is disposed between the corresponding pair of rotational connection bodies (31a, 31b) such that axes of the input shaft and the output shaft coincide with a center axis of a revolute pair formed between the proximal-end-side link hub and the proximal-side end link member, and the output shaft of the speed reduction mechanism is fixed to one rotational connection body of the pair of rotational connection bodies (31a, 31b), and the input shaft of the speed reduction mechanism is rotatably supported by the other rotational connection body of the pair of rotational connection bodies (31a, 31b). a proximal-end-side link hub; a distal-end-side link hub; at least three link mechanisms via which the distal-end-side link hub is connected to the proximal-end-side link hub so as to be changeable in position relative thereto, each link mechanism including a proximal-side end link member having one end pivotably coupled to the proximal-end-side link hub, a distal-side end link member having one end pivotably coupled to the distal-end-side link hub, and a center link member having opposite ends pivotably coupled to the other end of the proximal-side end link member and the other end of the distal-side end link member, respectively; each link mechanism including a proximal-side end link member having one end pivotably coupled to the proximal-end-side link hub, a distal-side end link member having one end pivotably coupled to the distal-end-side link hub, and a center link member having opposite ends pivotably coupled to the other end of the proximal-side end link member and the other end of the distal-side end link member, respectively; position-controlling actuators provided to two or more link mechanisms among the at least three link mechanisms, and each configured to arbitrarily change a position of the distal-end-side link hub relative to the proximal-end-side link hub; and speed reduction mechanisms each configured to reduce a speed of rotation and transmit a rotational power to the corresponding proximal-side end link member, wherein the proximal-side end link member includes a bent portion bent at an arbitrary angle, and a rotational connection portion (31A, 31B) disposed at one end of the bent portion and including a pair of rotational connection bodies (31a, 31b) arranged so as to be spaced from each other, each speed reduction mechanism includes an input shaft and an output shaft coaxial with each other, and is disposed between the corresponding pair of rotational connection bodies (31a, 31b) such that axes of the input shaft and the output shaft coincide with a center axis of a revolute pair formed between the proximal-end-side link hub and the proximal-side end link member, and the output shaft of the speed reduction mechanism is fixed to one rotational connection body of the pair of rotational connection bodies (31a, 31b), and the input shaft of the speed reduction mechanism is rotatably supported by the other rotational connection body of the pair of rotational connection bodies (31a, 31b).