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Notes: The target motions are a rotation of 1° and a translation of -0.6021 mm around and along the x-axis. Desired motions are shown in italic font and the parasitic ones are in regular font.

Table 5 Notes: The target motions are a rotation of 1° and a translation of -0.6021 mm around and along the x-axis. Desired motions are shown in italic font and the parasitic ones are in regular font.

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The primary and secondary components of the screw cannot be simultaneously null. For screws representing displacements, the pitch leads to a classification of three kinds of motions
The primary and secondary components of the screw cannot be simultaneously null. For screws representing displacements, the pitch leads to a classification of three kinds of motions
For instance, this relationship for a beam with a square cross-section can be of the form The global stiffness is computed in global coordinates. Therefore, the wrench in a master element has conveniently exchanged its vector components as WwW = QWinaster. Then, it is changed to global coordinates using
For instance, this relationship for a beam with a square cross-section can be of the form The global stiffness is computed in global coordinates. Therefore, the wrench in a master element has conveniently exchanged its vector components as WwW = QWinaster. Then, it is changed to global coordinates using
Table 3. Wrench systems of Table 1 that can be built with flexure beams The flexure beams cannot build all of the constraint spaces enumerated in Tables 1 and 2. In Tables 3 and 4, the constraint spaces that can be built are shown (Su and Tari, 2010). The asterisks in some cases of Table 4 indicate that their constraint space can only be built on condition that the pitch of one the desired twist screws has an opposite sign with respect to any other of the desired twist screws.
Table 3. Wrench systems of Table 1 that can be built with flexure beams The flexure beams cannot build all of the constraint spaces enumerated in Tables 1 and 2. In Tables 3 and 4, the constraint spaces that can be built are shown (Su and Tari, 2010). The asterisks in some cases of Table 4 indicate that their constraint space can only be built on condition that the pitch of one the desired twist screws has an opposite sign with respect to any other of the desired twist screws.
Notes: Target rotations are 1° around x and z axes, and target translations are 1 mm along the x and y axes. Desired motions are shown in italic font and the parasitic ones are in regular font. fable 5 Twist component values (linear and angular displacements) obtained for the R,-Rz-Tz-Ty flexure stage
Notes: Target rotations are 1° around x and z axes, and target translations are 1 mm along the x and y axes. Desired motions are shown in italic font and the parasitic ones are in regular font. fable 5 Twist component values (linear and angular displacements) obtained for the R,-Rz-Tz-Ty flexure stage
igure 3 Computed actuation wrench W,4; in the RRTT flexure stage (continued) (see online version for colours)
igure 3 Computed actuation wrench W,4; in the RRTT flexure stage (continued) (see online version for colours)
Figure 5 Geometric arrangement of the six constraint beams for the H flexure stage (see online version for colours) ep 5 The actuation wrenches are calculated using the stiffness matrix of the flexible mechanism, as shown in equation (21). Then, the actuation system 1
Figure 5 Geometric arrangement of the six constraint beams for the H flexure stage (see online version for colours) ep 5 The actuation wrenches are calculated using the stiffness matrix of the flexible mechanism, as shown in equation (21). Then, the actuation system 1
The wrench W, is not a pure force because the dot product between its primary vector f4 and its secondary vector M/, is non-zero. As a consequence, the acting force obtained does not belong to the 26 actuation systems identified by Hopkins (2010). The pitch of this force is calculated from equation (2) as g = —0.025225. Then, the actuation wrench W 4 can be decomposed into a pure force W 4, parallel to the x — y plane and a pure moment W,,,,, in the direction of the force
The wrench W, is not a pure force because the dot product between its primary vector f4 and its secondary vector M/, is non-zero. As a consequence, the acting force obtained does not belong to the 26 actuation systems identified by Hopkins (2010). The pitch of this force is calculated from equation (2) as g = —0.025225. Then, the actuation wrench W 4 can be decomposed into a pure force W 4, parallel to the x — y plane and a pure moment W,,,,, in the direction of the force
‘igure 6 Application of the actuation wrench W 4 on the guided point of the H flexure stage (see online version for colours)
‘igure 6 Application of the actuation wrench W 4 on the guided point of the H flexure stage (see online version for colours)
sure 6 Application of the actuation wrench W, on the guided point of the H flexure stage (continued) (see online version for colours) ‘able 6 Twist component values (linear and angular displacements) obtained for the H; flexure stage
sure 6 Application of the actuation wrench W, on the guided point of the H flexure stage (continued) (see online version for colours) ‘able 6 Twist component values (linear and angular displacements) obtained for the H; flexure stage
re 7 FEA static analysis H, (a) mesh (b) twist around (c) along the x axis, produced respectively by the components of a pure force actuating on the y and x directions and contained in the same plane (see online version for colours)
re 7 FEA static analysis H, (a) mesh (b) twist around (c) along the x axis, produced respectively by the components of a pure force actuating on the y and x directions and contained in the same plane (see online version for colours)
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MathematicsLinear AlgebraScrew Theory
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