Dr. Victor Zayas invented and patented the seismic isolator that is known under the Trade Name “Friction Pendulum Bearing®” in 1985, which together with Lead Rubber Bearing revolutionized modern seismic hardware. Prior to the expiration of Dr. Zayas's patent, Prof. Chong-Shien Tsai filed a patent in Taiwan (R.O.C.) in 1991, which represents an interesting evolution thereof. In all the seven (7) versions illustrated in the Prof. Tsai's Patent a hinged slider separates the two concave surfaces. At the turn of the last century, a further version of DCSS appeared in Japan, in which the slider is solid, in that the articulation has been removed. Being constructively much simpler, it has met with success with all seismic hardware manufacturers. However, this simplified version has produced serious anomalies. These consist of high eccentricities that produce significant deformations at the edges of the sliding material (liner) with its consequent wearing, as well as strong vibrations transmitted to the structure and even the phenomenon of "banging". The paper elaborates the mathematical models of the Kinematics of the two types of Double Curved Surface Sliders, identifies the critical parameters and quantifies the values ​​thereof that produce the observed adverse phenomena. Finally, the paper reports the list of factors, the concomitant presence of which suggests not adopting the simplified solution.