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This paper deals with the scaling factor's effect on the cantilever beam's natural frequency. Scaling a prototype dimension will make it easier to manufacture and test the dynamic characteristics of structures with enormous sizes. Natural frequency is one of the essential parameters of the vibration characteristics of the system. The phenomenon that often occurs in vibrating structures is the resonance phenomenon. Resonance is a system state in which an abnormally large vibration is generated in response to an external stimulus, happening when the frequency of the disturbance is equal to, or nearly identical to, the natural frequency of the system. This research investigates the scale factor on natural frequency using the analytical method using Euler-Bernoulli beam theory, the MSC Nastran/Patran software, and experimental testing using an impact hammer on a cantilever beam. The three methods were applied to beams with four scaling variations: 1:1, 1:2.04, 1:2.85, and 1:3.48. Based on the results, the natural frequencies increase by the size scale reduction value in the modeling. The natural frequency value in the actual structure has a value equivalent to 1/S of the natural frequency value of the scale, whereas S is defined as the downgrade scale value. This result follows the Similitude theory.

Pada paper ini dikaji optimasi postur mekanisme paralel 3-URU rotasi murni. Optimasi inidigunakan untuk memperoleh kekakuan kinematik yang optimal berupa kemampuanmekanisme meneruskan torsi input dan kemampuan mekanisme menahan gaya luar yangdinyatakan dengan indeks evaluasi (EI). Optimasi meliputi pemilihan parameter kinematikyang menggambarkan gerak platformyang dinyatakan dengan rotasi berurut berdasarkanEuler Angle dengan sistem rotasi Z-X-Z. Euler Angle tersebut dinyatakan dengan , , z x ? ? ? .Pada penelitian ini mekanisme paralel rotasi murni 3-URU diaplikasikan sebagaipengontrolan orientasi pahat pada mesin perkakas. Pada aplikasi ini sudut ? merupakansudut redundant yang menyatakan putaran pada sumbu yang tegak lurus terhadap bidangplatform. Berdasarkan hasil analisis diperoleh bahwa ? optimal merupakan fungsi sudutinklinasi platform ?()x yang dapat diformulasikan dengan6 5 4 3 2 1 -08( ) 4 -06( ) 0.0008( ) 0.0151( ) 0.3143( ? optimal ? ? E ?x ? E ?x ? ?x ? ?x ? ?x ) 3.9654( ) 79.977 x ? ? ? .Denganmenggunakan formulasi sudut redundant ini telah didapatkan kekakuan yang optimal yangdinyatakan dengan indek evaluasi EI.Kata kunci: kinematik, mekanisme paralel, constraint singularity, actuation singularity In this paper was studied the optimization of posture of a 3-URU spherical parallelmechanism. The mechanism was applied tocontrol the orentation of platform represented bythree successive Euler Rotation Angles. The rotation angle was denoted as ? , ? , ? z x thatindicates the rotation about Z, X dan Z axis respectively. Based on the desired aplication, thethird rotation angle, ? was recognized as redundant degree dof because such rotation is notrequired as orienting tool. The optimization was carried out to realize optimal kinematicstiffness of the mechanism to transmit the torques and to restrict the external forces acting onthe center of platform motion indicated by evaluation index, EI. Based onthis works, it wasobtained that the optimal ? is a function ofthe angle of inclinationplatform,? x formulated as6 5 4 3 2 1 -08( ) 4 -06( ) 0.0008( ) 0.0151( ) 0.3143( ) 3.9654( ) 79.977 optimal x x x x x x ? ? ? E ? ? E ? ? ? ? ? ? ? ? ? ? . The optimizegave the highes of EI.Keywords: kinematic, parallel mechanism, constraintsingularity, actuationsingularity