1. Date of download: 11/15/2017
Copyright © ASME. All rights reserved.
From: Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
J. Mechanisms Robotics. 2013;5(2): doi: /
Figure Legend:
(a) In the predictor step, a point p* in the tangent line to the curve at the current point pi is estimated. (b) In the corrector step, the predicted point p* is adjusted onto the curve producing a new point pi+1. (c) The drifting problem. (d) The cycling problem.

2. Date of download: 11/15/2017
Copyright © ASME. All rights reserved.
From: Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
J. Mechanisms Robotics. 2013;5(2): doi: /
Figure Legend:
(a) A four-bar linkage and (b) the coupler curve traced by a point affixed to one of its bars while taking the opposite one as fixed. (c) Any coupler curve generated by this linkage can be expressed in terms of its configuration space which can be represented by a one-dimensional variety in the space defined by {θ1,θ2,θ3}, or by {θ1,θ2} if the distance constraint between P3 and P4 is used as closure condition instead of the standard loop equation. (d) Alternatively, this configuration space can be represented by value ranges of a single variable, s2,3, one range for each combination of signs of the oriented areas of the triangles ΔP1P2P3 and ΔP2P4P3.

3. Date of download: 11/15/2017
Copyright © ASME. All rights reserved.
From: Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
J. Mechanisms Robotics. 2013;5(2): doi: /
Figure Legend:
(a) Using the standard vector loop formulation, the configuration space of a double butterfly linkage can be represented by a one-dimensional variety in the space defined by {θ1,…,θ7}. (b) Alternatively, using the proposed approach, this configuration space can be represented by a one-dimensional variety in the space defined by {s1,6,s2,4} which can be decomposed into 16 components, one for each combination of signs of the oriented areas of the triangles ΔP2P4P10,ΔP1P3P6,ΔP1P6P5, and ΔP4P9P7.

4. Date of download: 11/15/2017
Copyright © ASME. All rights reserved.
From: Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
J. Mechanisms Robotics. 2013;5(2): doi: /
Figure Legend:
Top: The bilateration problem. Bottom: Concatenation of two bilaterations.

5. Date of download: 11/15/2017
Copyright © ASME. All rights reserved.
From: Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
J. Mechanisms Robotics. 2013;5(2): doi: /
Figure Legend:
(a) In the strip of triangles {ΔP1P10P2,ΔP2P10P4,ΔP10P3P4},s1,3 can be obtained from bilaterations. (b) After affixing the strip of triangles {ΔP1P6P3,ΔP1P5P6,ΔP6P5P9} to the previous one, s4,9 can also be obtained using bilaterations. (c) Likewise, s2,6 can be obtained after affixing the strip of triangles {ΔP4P9P7,ΔP7P9P8}. (d) A double butterfly linkage. (e) If the lengths of dotted segments were known, this double butterfly linkage would be equivalent to the obtained structure resulting from attaching three strips of triangles.

6. Date of download: 11/15/2017
Copyright © ASME. All rights reserved.
From: Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
J. Mechanisms Robotics. 2013;5(2): doi: /
Figure Legend:
Top: The real solution set of Eq. (13) in the plane defined by s2,4 and s1,6 for sampled values of s2,4. Bottom: From left to right, the connected components of the configuration space traced when starting from the initial configurations s2,4=74, s1,6=188.68, and A2,4,10 > 0,A1,3,6 < 0,A1,6,5 < 0, and A4,9,7 < 0,s2,4=74,s1,6=122, and A2,4,10 > 0,A1,3,6 > 0,A1,6,5 > 0, and A4,9,7 < 0, and s2,4=74,s1,6=98.92, and A2,4,10 < 0,A1,3,6 < 0,A1,6,5 < 0, and A4,9,7 < 0, respectively.

7. Date of download: 11/15/2017
Copyright © ASME. All rights reserved.
From: Application of Distance Geometry to Tracing Coupler Curves of Pin-Jointed Linkages1
J. Mechanisms Robotics. 2013;5(2): doi: /
Figure Legend:
The paths followed by the revolute pair center P9 from different initial configurations. Top: For the curve traced from the initial configuration s2,4=74, s1,6=188.68, and A2,4,10 > 0,A1,3,6 < 0,A1,6,5 < 0, and A4,9,7  0,A1,3,6 > 0,A1,6,5 > 0, and A4,9,7 < 0, a cusp and a tacnode can be identified. Bottom: For the curve traced from the initial configuration s2,4=74,s1,6=98.92, and A2,4,10< 0,A1,3,6 < 0,A1,6,5 < 0, and A4,9,7 < 0, zoomed-in areas show how, after mapping the configuration space onto the workspace, several singular points are generated in a reduced region.