Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: One type of serial compliant mechanism (RPR) with variable stiffness actuators

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Joint twists in a serial mechanism. (a) For a prismatic joint, the joint twist ti is a unit vector along the prismatic joint axis. It is independent of the location of the joint. (b) For a revolute joint, the joint twist ti is orthogonal to the position vector ri and depends on the location of the joint.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Realization of a given compliance with a two-joint mechanism having a specified configuration. Joint twist t2 of J2 must be collinear with line l1⊥Kt1 at point O to realize the given C.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Relationship between joint twists ti and lines li. (a) If two joints are specified, the acceptable area for t3 is determined by lines l1 and l2. (b) Realization condition: t1 must be between and adjacent to lines l2 and l3; t2 must be between and adjacent to lines l1 and l3; and t3 must be between and adjacent to lines l1 and l2.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Geometric parameters of a PRR mechanism. The locus of J2 locations is line l, and the locus of J3 locations is circle C.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Extreme positions of a PRR mechanism. The extreme positions of link-3 occur when link-2 is parallel to line OO′. (a) Link-1 and link-2 are collinear, and J3 is at the intersection of line l1 and circle C. (b) Link-2 folds over link-1, and J3 is at the intersection of line l2 and circle C.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Geometric parameters of an RPR mechanism. L1 is the perpendicular distance from revolute joint J1 to the axis along which joint J3 is guided.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Extreme positions of an RPR mechanism. (a) The extreme position of link-1 occurs when J1A is parallel to link-3 (OJ3). (b) The extreme position of link-3 occurs when J3 is at the intersection point of circles C1 and C2. Link-3 cannot enter the interior of the shaded area.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Geometric parameters of an RRP mechanism. L3 is the (perpendicular) distance from the mechanism endpoint O to the prismatic axis.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Extreme positions of an RRP mechanism. The extreme position of link-3 occurs when prismatic joint J3 reaches circles C1 and C2. When J3 is on circle C1, link-1 and link-2 are fully extended. When J3 is on circle C2, link-2 folds over link-1.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Extreme positions of an RRP mechanism. (a) If θ3M does not exist, link-3 can rotate through θ3=180 deg in going from position θ3m to position −θ3m. (b) If θ3m does not exist, link-3 can rotate through θ3=0 in going from position θ3M to position −θ3M. For each case, prismatic joint J3 will pass through point A of link AB.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Geometric parameters of a PPR mechanism. The motion of link-3 is restricted by the limits of the two prismatic joints.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Geometric parameters of a PRP mechanism. The extreme positions can be determined by the limits of J1, L1M, and L1m.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: An RPP mechanism. Link-1 and link-3 have the same range of rotation variation.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: (a) A specified RRP mechanism having given link length L1=3. The position of joint base J1 relative to the compliance frame origin O is specified L0=2. (b) Configurations of the mechanism: Synthesis of C with two compliant joints J1 and J2 or J1 and J3.

Date of download: 10/30/2017 Copyright © ASME. All rights reserved. From: Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction J. Mechanisms Robotics. 2016;9(1):011005-011005-11. doi:10.1115/1.4035189 Figure Legend: Extreme positions of a PRP mechanism. The minimum angle of link-3 is determined by the upper limit of link-1, L1M.