The invention relates to shock and impact-attenuating hand grips.  More specifically, the invention relates to hand grips particularly suited for use with machines that tend to transmit shocks to the musculoskeltal extremities of the machine operator, such as the handle bars of motorcycles, off-road mountain bikes, all-terrain vehicles, and the like. 
In off-road cycling, whether self-propelled, as in mountain biking, or powered by an internal combustion engine, as in a motorcycle, or riding an all terrain vehicle (ATV), the rider tends to grip the handle bars tightly for balance and control.  Under competitive conditions, the rider may need to enhance his/her grip for prolonged periods of time while traversing difficult terrain conditions.  Such tight gripping by the rider tends to cause shocks and impacts, to be transferred to the rider's hands, wrists, forearms and related musculoskeletal extremities that need to twist as and the handle bars are pivoted toward and away from the rider.  Over a period of time, these various forces can induce fatigue, and fatigue can compromise riding enjoyment and competitive results in racing. 
Although attempts have been made to provide handle-bar grips that are comfortable to use, ones that are too-soft do not provide adequate motion control.  Ones that provide good motion control tend to be too-stiff to be comfortable.  Thus, there is a need for a handle bar grip that is comfortable to use, that provides precise motion control, that has good endurance, and that can be readily retro-fitted on existing handle bars. 
A primary object of the invention is to provide a novel hand grip assembly that includes a durable mounting sleeve located between an outer elastomeric grip and an inner handle bar for attenuating shocks and vibrations from the handle bar and for accommodating precise movement of the handle bar while being gripped tightly by the user.