On impulsive motion, braking and robotry

Newtonian dynamics is applied to impulsive motion. The third time derivativ e (x) triple over dot is introduced. By extending the concept of impulse I, I = integral(0)(tau) m(x) double over dot dt = m(x) over dot \(tau) - m(x) over dot\(0), the concept of jumpulse J is defined as {(J(i), tau(i))\J(i) equivalent to integral(tau i) m (x) triple over dot dt with m (x) triple over dot greater than or equal to 0 (or m (x) triple ove r dot less than or equal to 0) in the entire interval tau(i)}. The application of the concepts I and J to braking mechanisms in robotry is briefly discussed. The merit of introducing the jumpulse J [Eq. (7) in the text] is that we ca n now design the size and shape of the jumpulse for a given purpose by desi gning the F with the needed dF/dt within the interval tau; i.e., we are now refining our treatment of impulsive forces of the past, so that we have th e proper jumpulse for different purposes in different situations. The possi bility of fine braking devices may play a very important role in the develo pment of robotry in the future.