A spherical coordinates manipulating mechanism comprising an outer frame assembly, an inner frame assembly, four outer arc-link sets each including an outer arc-link, four inner arc-link sets each including an inner arc-link, and at least one effector arc-link set, wherein: the outer frame assembly comprises an outer frame including a plurality of brackets and four outer rotating members mounted to the outer frame wherein the outer frame has four vertexes geometrically defined by an outer tetrahedron, vertex-to-center lines of the outer tetrahedron are coincided with a center of the outer frame, and an axis of the outer rotating member is coincided with a vertex-to-center line of the outer tetrahedron; the inner frame assembly comprises an inner frame including a plurality of brackets and four inner rotating members mounted to the inner frame wherein the inner frame has four vertexes geometrically defined by an inner tetrahedron, vertex-to-center lines of the inner tetrahedron are coincided with a center of the inner frame, the center of the inner frame is coincided with the center of the outer frame, and an axis of the inner rotating member is coincided with a vertex-to-center line of the inner tetrahedron; the outer arc-link has an outbound end pivotally connected to one of the outer rotating members through an outer axle, and an inbound end pivoted with an outbound end of the inner arc-link through a middle axle wherein both the outer axle and the middle axle are coincided with the center of the outer frame; the inner arc-link has an inbound end pivotally connected to one of the inner rotating members through an inner axle wherein the inner axle is coincided with the center of the inner frame; sum of arc lengths of the outer arc-link i.e. angles α i and its corresponding inner arc-link i.e. angles β i is less than or equal to 180° sum of arc lengths of any two of the outer arc-links is greater than or equal to an angle between their corresponding vertex-to-center lines of the outer frame; sum of arc lengths of any two of the inner arc-links is greater than or equal to an angle between their corresponding vertex-to-center lines of the inner frame; characterized in that each of the at least one effector arc-link set comprises an effector arc-link and an effector rotating member and an end effector; wherein the effector arc-link is pivotally connected to the outer frame and pivots with outbound end of an outer arc-link, and an axis of outbound end of the effector arc-link is coincided with a vertex-to-center line of the outer tetrahedron for concentrically rotating around an orbit between inner frame and each inner arc-links; wherein the end effector is radially disposed on inboard of inbound end of the effector arc-link; wherein the effector rotating member is pivotally connected on outboard of inbound end of the effector arc-link and radially pivots with the end effector; and arc length of the effector arc-link is less than or equal to 90°. the outer frame assembly comprises an outer frame including a plurality of brackets and four outer rotating members mounted to the outer frame wherein the outer frame has four vertexes geometrically defined by an outer tetrahedron, vertex-to-center lines of the outer tetrahedron are coincided with a center of the outer frame, and an axis of the outer rotating member is coincided with a vertex-to-center line of the outer tetrahedron; the inner frame assembly comprises an inner frame including a plurality of brackets and four inner rotating members mounted to the inner frame wherein the inner frame has four vertexes geometrically defined by an inner tetrahedron, vertex-to-center lines of the inner tetrahedron are coincided with a center of the inner frame, the center of the inner frame is coincided with the center of the outer frame, and an axis of the inner rotating member is coincided with a vertex-to-center line of the inner tetrahedron; the outer arc-link has an outbound end pivotally connected to one of the outer rotating members through an outer axle, and an inbound end pivoted with an outbound end of the inner arc-link through a middle axle wherein both the outer axle and the middle axle are coincided with the center of the outer frame; the inner arc-link has an inbound end pivotally connected to one of the inner rotating members through an inner axle wherein the inner axle is coincided with the center of the inner frame; sum of arc lengths of the outer arc-link i.e. angles α i and its corresponding inner arc-link i.e. angles β i is less than or equal to 180° sum of arc lengths of any two of the outer arc-links is greater than or equal to an angle between their corresponding vertex-to-center lines of the outer frame; sum of arc lengths of any two of the inner arc-links is greater than or equal to an angle between their corresponding vertex-to-center lines of the inner frame; characterized in that each of the at least one effector arc-link set comprises an effector arc-link and an effector rotating member and an end effector; wherein the effector arc-link is pivotally connected to the outer frame and pivots with outbound end of an outer arc-link, and an axis of outbound end of the effector arc-link is coincided with a vertex-to-center line of the outer tetrahedron for concentrically rotating around an orbit between inner frame and each inner arc-links; wherein the end effector is radially disposed on inboard of inbound end of the effector arc-link; wherein the effector rotating member is pivotally connected on outboard of inbound end of the effector arc-link and radially pivots with the end effector; and arc length of the effector arc-link is less than or equal to 90°.