A safety brake (40,42) for controlling the rate of deceleration of a free-falling conveyance operating upon shaft guides (14,16) fixed within a mine shaft having a substantial vertical component, said safety brake (40,42) comprising: an activation system operable for supporting the conveyance during normal travel of the conveyance upon the shaft guides (14,16) and storing activation energy while supporting the conveyance, said activation system further operable for detecting a conveyance suspension failure or slack rope condition associated with a free-falling or obstructed condition of the conveyance, and said activation system further operable for releasing said activation energy upon detecting said conveyance suspension failure or slack rope condition to activate said safety brake; at least one guide clamp assembly disposed in communication with said activation system and operable to substantially self-lock onto a shaft guide (14,16) upon activation by the activation system; at least one brake path (166, 168, 170, 172) fixedly attached upon the conveyance; and at least one brake caliper assembly disposed in communication with said at least one guide clamp assembly and disposed for traveling engagement with said at least one brake path (166, 168, 170, 172); wherein said release of said activation energy by said activation system causes said at least one guide clamp assembly to be released from a standby condition and to substantially self-lock onto a shaft guide (14, 16), causing said at least one brake caliper assembly to travel upwardly upon said at least one brake path as the conveyance falls downwardly, characterized in that said upward travel of said at least one brake caliper assembly upon said at least one brake path (166, 168, 170, 172) is operable for generating increasing braking forces by said at least one brake caliper assembly upon said at least one brake path (166, 168, 170, 172) in a controlled manner, thereby bringing the conveyance to a stop; and in that the at least one guide clamp assembly has a tapered profile and is configured to travel upwardly and inwardly toward the shaft guide (14,16) upon activation by the activation system as the conveyance falls downwardly, so as to provide increased self-locking engagement by the guide clamp assembly upon the shaft guide (14,16). an activation system operable for supporting the conveyance during normal travel of the conveyance upon the shaft guides (14,16) and storing activation energy while supporting the conveyance, said activation system further operable for detecting a conveyance suspension failure or slack rope condition associated with a free-falling or obstructed condition of the conveyance, and said activation system further operable for releasing said activation energy upon detecting said conveyance suspension failure or slack rope condition to activate said safety brake; at least one guide clamp assembly disposed in communication with said activation system and operable to substantially self-lock onto a shaft guide (14,16) upon activation by the activation system; at least one brake path (166, 168, 170, 172) fixedly attached upon the conveyance; and at least one brake caliper assembly disposed in communication with said at least one guide clamp assembly and disposed for traveling engagement with said at least one brake path (166, 168, 170, 172); wherein said release of said activation energy by said activation system causes said at least one guide clamp assembly to be released from a standby condition and to substantially self-lock onto a shaft guide (14, 16), causing said at least one brake caliper assembly to travel upwardly upon said at least one brake path as the conveyance falls downwardly, characterized in that said upward travel of said at least one brake caliper assembly upon said at least one brake path (166, 168, 170, 172) is operable for generating increasing braking forces by said at least one brake caliper assembly upon said at least one brake path (166, 168, 170, 172) in a controlled manner, thereby bringing the conveyance to a stop; and in that the at least one guide clamp assembly has a tapered profile and is configured to travel upwardly and inwardly toward the shaft guide (14,16) upon activation by the activation system as the conveyance falls downwardly, so as to provide increased self-locking engagement by the guide clamp assembly upon the shaft guide (14,16).