A numerical approach for solving problems in robotic arm movement

Figures & data

Table 1. Results of the mechanical robotic arm model for and Relative Error for R.K. Ode45.

Solution Number	Time second	Exact Solution	R.K. Ode15s	R.K. Ode45	R.K. ode23tb	Error
1	0.0	−1.0000	−1.0000	−1.0000	−1.0000	0
2	0.5	−0.9742	−0.9773	−0.9773	−0.9773	0.318209813
3	1.0	−0.8942	−0.9069	−0.9069	−0.9069	1.420263923
4	1.5	−0.7576	−0.7867	−0.7866	−0.7867	3.827877508
5	2.0	−0.5641	−0.6164	−0.6163	−0.6164	9.253678426

Table 2. Results of the mechanical robotic arm model for and Relative Error for R.K. Ode45.

Solution Number	Time second	Exact Solution	RK Ode15s	RK Ode45	RK ode23tb	Error
1	0.0	0.0000	0.0000	0.0000	0.0000	0.0000
2	0.5	0.1045	0.0920	0.0920	0.0920	11.96172249
3	1.0	0.2161	0.1901	0.1903	0.1902	11.93891717
4	1.5	0.3304	0.2908	0.2909	0.2909	11.95520581
5	2.0	0.4426	0.3896	0.3898	0.3897	11.92950746

Table 3. Results of the mechanical robotic arm model for and Relative Error for R.K. Ode45.

Solution Number	Time second	Exact Solution	R.K. Ode15s	R.K. Ode45	R.K. ode23tb	Error
1	0.0	−1.0000	−1.0000	−1.0000	−1.0000	0
2	0.5	−0.9986	−0.9986	−0.9986	−0.9986	0
3	1.0	−0.9945	−0.9946	−0.9946	−0.9946	0.010055304
4	1.5	−0.9881	−0.9882	−0.9882	−0.9882	0.010120433
5	2.0	−0.9793	−0.9795	−0.9795	−0.9795	0.020422751

Table 4. Results of the mechanical robotic arm model for and Relative Error for R.K. Ode45.

Solution Number	Time second	Exact Solution	R.K. Ode15s	R.K. Ode45	R.K. ode23tb	Error
1	0.0	0.0000	0.0000	0.0000	0.0000	0
2	0.5	0.0054	0.0054	0.0054	0.0054	0
3	1.0	0.0105	0.0105	0.0105	0.0105	0
4	1.5	0.0153	0.0152	0.0152	0.0152	0.653594771
5	2.0	0.0198	0.0194	0.0194	0.0194	2.02020202

Figure 1. Position q₁ at joint (1).

Figure 2. Position q₂ at joint (2).

Figure 3. Velocity on joint/1.

Figure 4. Velocity on joint/2.