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Inverse Kinematics Synthesis: Computing of S1, S2, S3 from Cylindrical Coordinates, R, Z, θ

Excerpt

The previous chapter, chapter 5, formulated the inverse kinematics equations that gave servo angles, S1, S2, S3 as functions of R, Z, θ. This chapter now formulates how to compute these functions, which are largely trigonometrical functions, with an integer-only 16-bit computer, namely the Basic Stamp microcomputer. The chapter concludes with the complete code for controlling one 3dof leg. Computation will only call upon four arithmetic instructions, which are, addition, subtraction, multiplication and division. Trigonometrical functions will not be called upon because, (i) the Basic Stamp does not possess such instructions, (ii) they are not needed and (iii) trigonometrical functions have non-unique solutions. Instead, we will compute the inverse kinematics equations using piecewise truncated Taylor series that rely solely on the ability to add, subtract, multiply and divide integer numbers as shown with equation 6.1, which is a 3-variable Taylor series equation.

6.1Introduction
6.2The piecewise construction of the cylindrical coordinate frame
6.3Computing the S1 servo angle with 1st and 2nd order equations
6.4Computing the S2 and S3 servos with 1st order equations
6.5Example computing of S2 in T7 sector
6.6Servo S3 computation
6.7Corrections
Topics: Kinematics

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