MlZ+Kr^ Z = K^-jix 



Z(t) 



X(t) 



J_ 



MZ + KZ = KX 



where M = Mi 



K= Ku L,/L 



(a) 



Figure 1. Single-degree-of-freedom model of MCLS. 



of the uncertainty of the coefficients at the time the 

 model was developed, they were omitted; this model 

 was intended to produce only gross approximations. 

 Physically, the MCLS (Motion Compensating Lift 

 System) is arranged as shown in Figure la with the 

 boom, pivoted at one end, supported by the spring 

 Kg at a distance Lj from the pivot point. The boom 

 supports a payload Mj^ on a rigid cable suspended 

 from the outer end at a distance L from the pivot 

 point. Motion of the support platform is represented 

 by X(t) and motion of the payload by Z(t). This 

 model is mathematically equivalent to the simple 

 spring/mass system of Figure lb in which the input 

 motion is X(t) and the response Z(t). The ratio of the 

 amplitude of the load motion Z(t) to the input 

 motion X(t) (that is, the response of this system) is 

 shown in Figure 2 as a function of the period of the 

 input T divided by the resonance period T^. Damping, 

 or drag, forces present at the payload tend to 

 decrease system response while damping in the com- 

 pensator mechanism tends to increase system 

 response by increasing the magnitude of the forces 

 acting on the lift line at the boom tip. 



Later models used by CEL included those shown 

 in Figures 3 and 4, with the latter being programmed 

 for computer-based analysis. The criteria used in the 

 design of the MCLS included minimizing internal 

 friction and damping in the compensator unit and 

 keeping the system's resonant period r^ significantly 

 larger than the expected periods of the input X(t). 

 These criteria tend to reduce system response, and 

 thus to improve system performance. With the system 

 designed so that the value of K is small, the dynamic 

 line-tension variations are kept within the desired 

 limits (Table 1). 



The contractor's analytical model (Figure 5) is 

 similar to CEL's but incorporates damping factors in 

 the spring system and at the payload and also 

 includes the mass and elasticity of the cable in a 

 simple, tvv'o-segment, lumped-mass approximation. A 

 mathematical description of this system was 

 developed with this model, resulting in the four 

 simultaneous second-order differential equations 

 below 



