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In this chapter, Eq. ( 2.4 ) of the forward kinematics is treated as follows, \(\displaystyle {\mathbf {T}}_{\mathcal {D}}(b_1,\,\theta _2,\,b_3)={\mathcal D}_1(b_1){\mathcal D}_2(\theta _2){\mathcal D}_3(b_3) {} \) which indicates that \({\mathbf {T}}_{\mathcal D}\) is function of the joint variables \(b_1\) , \(\theta _2\) and \(b_3\) . For the given parameters, which in general \(0\leq \theta _1,\,\theta _3\leq 2\pi \) , \(b_2\) and \(a_i\in \mathbb {R}^+\) , where \(i=1,\,2,\,3\) . In some cases, there will be restricted values of \(\theta _1\) and \(\theta _3\) , which will be indicated when applied, and, as mentioned in Sect. 3.1 , \(\alpha _1\) and \(\alpha _2\) take only 0, 90, 180, and 270 degrees.

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PRP Arrangement

  • 章节

  • 发表日期：

    2026年

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  • Max Antonio González-Palacios

摘要

In this chapter, Eq. ( 2.4 ) of the forward kinematics is treated as follows, \(\displaystyle {\mathbf {T}}_{\mathcal {D}}(b_1,\,\theta _2,\,b_3)={\mathcal D}_1(b_1){\mathcal D}_2(\theta _2){\mathcal D}_3(b_3) {} \) which indicates that \({\mathbf {T}}_{\mathcal D}\) is function of the joint variables \(b_1\) , \(\theta _2\) and \(b_3\) . For the given parameters, which in general \(0\leq \theta _1,\,\theta _3\leq 2\pi \) , \(b_2\) and \(a_i\in \mathbb {R}^+\) , where \(i=1,\,2,\,3\) . In some cases, there will be restricted values of \(\theta _1\) and \(\theta _3\) , which will be indicated when applied, and, as mentioned in Sect. 3.1 , \(\alpha _1\) and \(\alpha _2\) take only 0, 90, 180, and 270 degrees.