Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Table 2

First ten natural frequencies (Hz); two-link manipulator, see Table 1; (𝐿₁/ℎ=833.3, 𝐿_𝑇/ℎ=1733).

	𝜃2 = 0°					𝜃2 = 45°					𝜃2 = 90°
Mode	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡
1	0.2002	0.2002	0.2002	0.00	0.00	0.2114	0.2114	0.2114	0.00	0.00	0.2490	0.2490	0.2490	0.00	0.00
2	0.9557	0.9557	0.9557	0.00	0.00	0.8269	0.8269	0.8269	0.00	0.00	0.6531	0.6531	0.6531	0.00	0.00
3	4.8901	4.8901	4.8901	0.00	0.00	4.8558	4.8558	4.8558	0.00	0.00	4.8255	4.8255	4.8255	0.00	0.00
4	9.0744	9.0744	9.0744	0.00	0.00	8.9924	8.9924	8.9924	0.00	0.00	8.9161	8.9161	8.9161	0.00	0.00
5	14.500	14.500	14.499	0.01	0.01	14.460	14.460	14.460	0.00	0.00	14.428	14.428	14.428	0.00	0.00
6	20.650	20.650	20.650	0.00	0.00	20.579	20.579	20.578	0.00	0.00	20.535	20.535	20.534	0.00	0.00
7	36.447	36.447	36.446	0.00	0.00	36.298	36.298	36.297	0.00	0.00	36.150	36.150	36.149	0.00	0.00
8	36.746	36.746	36.745	0.00	0.00	36.756	36.756	36.755	0.00	0.00	36.812	36.812	36.811	0.00	0.00
9	62.872	62.872	62.870	0.00	0.00	62.759	62.760	62.757	0.00	0.00	62.682	62.682	62.680	0.00	0.00
10	70.917	70.917	70.914	0.00	0.00	70.870	70.870	70.867	0.00	0.00	70.842	70.842	70.839	0.00	0.00

^†Through the model by di Castri et al. [12] ^‡Through implementation of the model by Milford and Asokanthan [11].