Vibration Analysis of Multilink Manipulators Based on Timoshenko Beam Theory

Table 3

First ten natural frequencies (Hz); two-link manipulator; (𝐿₁/ℎ=83.33, 𝐿_𝑇/ℎ=173.3).

	𝜃2= 0°					𝜃2 = 45°					𝜃2 = 90°
Mode	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡	EB ^†	EB ^‡	T	Δ^†	Δ^‡
1	3.9344	3.9344	3.9343	0.00	0.00	4.1907	4.1907	4.1906	0.00	0.00	5.0987	5.0987	5.0986	0.00	0.00
2	21.550	21.550	21.546	0.02	0.02	17.925	17.926	17.923	0.01	0.02	13.554	13.554	13.552	0.01	0.01
3	70.720	70.720	70.695	0.04	0.04	68.901	68.908	68.878	0.03	0.04	68.120	68.130	68.098	0.03	0.05
4	130.00	130.00	129.91	0.07	0.07	122.38	122.41	122.29	0.07	0.10	117.10	117.11	117.01	0.08	0.09
5	218.26	218.26	218.07	0.09	0.09	214.44	214.52	214.26	0.08	0.12	212.37	212.43	212.19	0.08	0.11
6	317.00	317.00	316.59	0.13	0.13	308.98	309.23	308.56	0.14	0.22	304.46	304.57	304.03	0.14	0.18
7	425.34	425.34	424.49	0.20	0.20	418.99	419.31	418.17	0.20	0.27	415.96	416.06	415.15	0.20	0.22
8	545.20	545.20	544.05	0.21	0.21	536.96	537.95	535.81	0.21	0.40	534.21	534.97	533.05	0.22	0.36
9	745.10	745.10	742.10	0.40	0.40	734.87	736.49	731.95	0.40	0.62	731.71	732.18	728.79	0.40	0.47
10	837.96	837.96	835.26	0.32	0.32	826.94	830.08	824.25	0.33	0.71	825.38	827.93	822.68	0.33	0.64

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