Kinematics Analysis of a Novel Five-Degree-of-Freedom Spatial Parallel Micromanipulator

Table 1

Example results of the inverse kinematics for rotational movement of the piezoelectric actuators.

	Angles
	𝛿1 [°]	𝛿2 [°]	𝛿3 [°]	𝛿1 [°]	𝛿2 [°]	𝛿3 [°]	𝛿1 [°]	𝛿2 [°]	𝛿3 [°]	𝛿1 [°]	𝛿2 [°]	𝛿3 [°]
Mathematica	17.10	25.43	10.59	12.15	17.85	6.39	6.53	9.33	2.88	1.39	1.92	0.53
Cabri 3D	16.89	25.73	10.51	12.14	17.98	6.26	6.56	9.35	2.82	1.40	1.92	0.52
Error	0.21	−0.30	0.08	0.01	−0.13	0.13	−0.03	−0.02	0.06	−0.01	0.00	0.01
α		−15 °			−10 °			−5 °			−1 °
β		−15 °			−10 °			−5 °			−1 °
Mathematica	26.91	5.41	30.22	16.65	4.10	20.07	7.68	2.31	9.90	1.44	0.51	1.94
Cabri 3D	25.85	5.82	29.94	16.23	4.26	19.94	7.56	2.42	9.88	1.44	0.51	1.94
Error	1.06	−0.41	0.28	0.42	−0.16	0.13	0.12	−0.11	0.02	0.00	0.00	0.00
α		15 °			10 °			5 °			1 °
β		−15 °			−10 °			−5 °			−1 °
Mathematica	16.88	10.59	25.43	12.15	6.37	17.85	6.53	2.88	9.33	1.39	0.53	1.92
Cabri 3D	17.10	10.56	25.81	12.17	6.39	18.01	6.58	2.87	9.39	1.40	0.53	1.93
Error	−0.22	0.03	−0.38	−0.02	−0.02	−0.16	−0.05	0.01	0.06	−0.01	0.00	−0.01
α		−15 °			−10 °			−5 °			−1 °
β		15 °			10 °			5 °			1 °
Mathematica	26.91	30.22	5.41	16.65	20.07	4.10	7.68	9.90	2.31	1.43	1.94	0.50
Cabri 3D	25.85	29.97	5.76	16.24	19.97	4.21	7.59	9.91	2.32	1.44	1.94	0.51
Error	1.06	0.25	−0.35	0.41	0.10	−0.11	0.09	−0.01	−0.01	−0.01	0.00	−0.01
α		15 °			10 °			5 °			1 °
β		15 °			10 °			5 °			1 °