CHAPTER IX 



MECHANICS OF LOCOMOTION IN THE EVOLUTION OF LIMB STRUCTURE AS BEARING 

 ON THE FORM AND HABITS OF THE TITANOTHERES AND THE RELATED ODD-TOED 

 UNGULATES 



The facts presented in this chapter should be 

 studied in connection with those given in Chapter 

 VIII on musculature and bone structure. Together 

 these sections afford a complete interpretation of the 

 mechanical evolution of the titanotheres. 



SECTION 1. ADAPTATION TO LOCOMOTION IN THE 

 LIMBS OF THE FLEET (CURSORIAL) AND THE 

 PONDEROUS (GRAVIPORTAL) TYPES OF TITANO- 

 THERES AND OTHER HOOFED QUADRUPEDS 



MECHANICAI AND PHYSIOLOGICAL PRINCIPLES GOVERN- 

 ING THE PROPORTIONS AND ANGULATION OF LIMB 

 SEGMENTS IN GRAVIPORTAL UNGULATES 



RESEARCHES MADE AND PRINCIPLES ESTABLISHED 



The laws of limb adaptation here presented are the 

 result partly of joint and partly of independent re- 

 searches made for this monograph. In 1900 Osborn 

 (1900.181) independently established the relations of 

 the articular facets and joints to speed and weight, 

 and in 1911 he planned a comparative measurement 

 and investigation of the limbs and arches in the nine 

 families of perissodactyls and other ungulates. Osborn 

 and Gregory jointly established the laws of limb 

 proportion in adaptation to speed and weight, re- 

 spectively, which were in part published in advance 

 by Gregory (1912.1). Gregory (1912) independently 

 investigated and applied the mechanics of muscular 

 limb action and leverages in relation to speed and 

 weight. The text of this chapter has been jointly 

 prepared by Osborn and Gregory. 



The principle that the limbs of quadrupeds are 

 compound levers and that the relative lengths of the 

 upper, middle, and lower segments are adapted to 

 specific muscular powers, loads, and speeds is applied 

 in the present monograph to the elucidation of the 

 adaptive contrasts between cursorial and graviportal 

 ungulates. 



The limb movements of living animals have been 

 investigated by Borelli (1680.1), Marey (1874.1), 

 Stillman (1882.1), Haycraft (1900.1), Luciani (1905.1), 

 Muybridge (1907.1). From the evolutionary point of 

 view there are the studies of Cope (1889.3), Osborn 

 (1890.51, 1895.99, 1900.181), Gaudry (1906.1), Greg- 

 ory (1912.1). Cope made some suggestions as to the 

 relative length of limb segments in saltatorial, cursorial, 

 and graviportal types. Osborn especially developed 

 the subject of angulation of the limbs in relation to 

 great weight and to the articular planes of the proximal 

 and distal limb facets. Gaudry pointed out the limb 



convergence between such straight-limbed, ponderous 

 ungulates as Elephas, Uintatherium, and Pyrotherium 

 as well as the convergence between numerous curso- 

 rial animals {Equus, Theosodon). Matthew (1909.1, 

 pp. 429-432) discussed the ratios of the limb seg- 

 ments in various carnivores and ungulates, in adap- 

 tation to cursorial and "rectigrade" modes of locomo- 

 tion. Riitimeyer and Allen (1876) discussed the 

 relative lengths of the different segments of the fore 

 and hind limbs in the extinct and living species of 

 the bison and introduced the ratio method for taxo- 

 nomic purposes. This method was effectively used 

 by Gidley (1903.1) in comparing the different genera 

 and species of Equidae. A review of the mechanical 

 principles of quadrupedal locomotion with special 

 reference to the limbs of ungulates is given by 

 Gregory (1912.1, pp. 268-269). The chief works are 

 cited in the bibliography for this chapter. 



PRINCIPLES OP LEVERAGE AND MUSCULAR ACTION 

 By William K. Gregoky 



The meaning of contrasting limb proportions and 

 angulation in cursorial and graviportal animals be- 

 comes clear if we keep in mind the underlying mechan- 

 ical and physiological facts and principles. 



Observation and photographs of animals in motion 

 at once reveal the simple fact that the limbs by sud- 

 denly straightening out and opening the angles at 

 the joints raise the whole body and not only enable 

 it to fall forward but alternately accelerate and check 

 the action of gravity. An animal running on a 

 treadmill reveals the almost equally important fact 

 that the limbs when extended anteriorly tend to drag 

 the ground backward and to pull the body forward. A 

 standing horse might give the impression that the fore 

 limbs were relatively passive props and that the hind 

 limbs were the chief propellers, but . a consideration 

 of the action of the massive muscles of the fore limbs 

 and study of a horse running on a treadmill show that 

 the fore limbs also exert great strength in dragging the 

 body forward, in raising the fore part of the body, and 

 even in pushing it forward when the fore limb is ex- 

 tended backward. In most ungulates the fore limbs 

 sustain the greater loads. 



When the limbs are moving quickly they seem to 

 swing with the regularity of a penduhmi, and it has 

 often been noted that in cursorial animals the limb 

 muscles are bunched or concentrated toward the proxi- 

 mal or upper end of the limb, the muscles being pro- 



727 



