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This paper formulates and solves the design equations for three degree-of-freedom spatial serial chains constructed with two revolute (R) joints and one prismatic (P) joint. Previous work has shown that equating the kinematics equations of the chain to a set of end-effector positions yields 24 equations in 25 unknowns, which means one of the design...
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Citations
... Every robot can be described by its DH table. For a more exhaustive review of the Denavit-Hartenberg Representation see references [1] and [2]. ...
... Two user defined algorithms were developed using MATLAB for Joint space and Cartesian space tracking [2]. The limitations of the above works are: ...
... Shoulder joint angle θ 2 We know that, cos (A+B) = cos A cos Bsin A sin B sin (A+B) = sin A cos B + cos A sin B Let us consider A = θ 2, B = θ 3 c 23 = c 2 c 3s 2 s 3 s 23 = s 2 c 3 + c 2 s 3 From equations (5) and (6) we get, c 2 c 3s 2 s 3 +c 2 = (c 1 p x + s 1 p y -a 1 -c 234 d 5 )/ a 3 s 2 c 3 +c 2 s 3 +s 2 = (-p z +d 1 -s 234 d 5 )/ a 3 (c 3 +1) c 2 -s 3 s 2 = (c 1 p x +s 1 p y -a 1 -c 234 d 5 )/a 3 (8) s 3 c 2 + (c 3 +1) s 2 = (-p z +d 1 -s 234 d 5 )/a 3 (9) Reduce equations (8) and (9) to find s 2, (8) x a 3 s 3 a 3 s 3 (c 3 +1) c 2 -a 3 s 3 2 s 2 =s 3 (c 1 p x + s 1 p y -a 1 -c 234 d 5 ) (10) (9) x a 3 (c 3 +1): a 3 s 3 (c 3 +1)c 2 +a 3 (c 3 +1) 2 s 2 =(c 3 +1)(-p z +d 1 -s 234 d 5 ) (11) To eliminate s 2, subtract equation (10) from Equation (11) ((c 3 +1) 2 +s 3 2 ) a 3 s 2 = (c 3 +1) (-p z +d 1 -s 234 d 5 )-s 3 (c 1 p x + s 1 p y -a 1c 234 d 5 )) s 2 = (c 3 +1) (-p z +d 1 -s 234 d 5 ) -s 3 (c 1 p x + s 1 p y -a 1 -c 234 d 5 )/ a 3 ((c 3 +1) 2 +s 3 2 ) again reduce Equations (8) and (9) to find c 2 (8) x a 3 (c 3 +1): a 3 (c 3 +1) 2 c 2a 3 (c 3 +1) s 3 s 2 = (c 3 +1) (c 1 p x + s 1 p y -a 1 -c 234 d 5 ) (12) (9) x a 3 s 3: a 3 s 3 2 c 2 + a 3 (c 3 +1) s 2 s 3 =s 3 (-p z +d 1 -s 234 d 5 ) (13) To eliminate c 2, add Equation (12) and Equation (13) a 3 c 2 ((c 3 +1) 2 + s 3 2 ) = (c 3 +1) (c 1 p x + s 1 p y -a 1 -c 234 d 5 ) + s 3 (p z +d 1 -s 234 d 5 ) c 2 = ((c 3 +1) (c 1 p x + s 1 p y -a 1 -c 234 d 5 ) + (s 3 (-p z +d 1 -s 234 d 5 ))/ a 3 ((c 3 +1) 2 + s 3 2 ) t 2 = s 2 / c 2 = (c 3 +1) (-p z +d 1 -s 234 d 5 ) -s 3 (c 1 p x + s 1 p y -a 1 -c 234 d 5 )/ ((c 3 +1) (c 1 p x + s 1 p y -a 1 -c 234 d 5 ) + (s 3 (-p z +d 1 -s 234 d 5 )) θ 2 = atan2 ([((c 3 +1) (-p z +d 1 -s 234 d 5 )/ a 3 )-(s 3 (c 1 p x + s 1 p y -a 1c 234 d 5 )/ a 3 )/ ((c 3 +1) 2 +s 3 2 ) ],[( (c 3 +1) (c 1 p x + s 1 p y -a 1 -c 234 d 5 )/ a 3 )+ (s 3 (-p z +d 1 -s 234 d 5 )/ a 3 ) /((c 3 +1) 2 +s 3 2 )]) ...
The joint arrangement of every robot can be described by the Denavit Hardenberg parameters. These parameters are enough to obtain a working of the robot described and Presented is a Matlab program which modelled Sorbet era 5u pluse given a set of corresponding DH parameters. The prim aim of this paper is to develop forward and inverse kinematic models of Sorbet era 5u plus using Matlab GUI in order to optimize the manipulative task execution. Forward kinematics analysis is done for the flexible twist angle, link lengths, and link offsets of each joints by varying joint angles to specify the position and orientation of the end effectors. Forward analysis can be used to provide the position of some point on the end effectors together with the orientation of the end effectors measured relative to a coordinate system fixed to ground for a specified set of joint variables. This simulation allows the user to get forward kinematics and inverse kinematics of Scorbot era 5u Plus of the modelled robot in various link length parameters and joint angles and corresponding end effectors position and orientation is going to validate with Rob cell software and compared with Lab view measured values.
... [53], [54], [55], [56], dual quaternion synthesis, e.g. [57], [58], or also factorization methods e.g. [32] exist, which will not be used in this work, however. ...
This dissertation presents a novel task-based approach towards computer-aided kinematic design of spherically constrained kinematic chains. Based on a detailed review of the state-of-the-art in theoretical kinematics, linkage design theory as well as computer-aided kinematic design new kinematic synthesis and analysis methods as well as a general CAD-integrated kinematic design process were developed. An example of a spatial kinematic motion task is used to demonstrate theory and methods.
... As presented in [14], ...
Upon the appearance of nylons, silicon, tendons, smart and soft materials, wearable robotics is going closer to the human body, leading robotics and biomechanics to provide us new physical rehabilitations and improvements. In the area that concerns soft robotic prosthesis, the main challenge is the design of well sized mechatronic limbs and smart controllers that should help people to achieve desired movements. As a consequence, we present a hybrid model that allows different ways of representing hand poses, according to special interactions that arise from soft robotics chains. Our hybrid model uses the positions of finger's parts computed with the Denavit-Hartenberg (DH) method mixed with the quaternions representation to avoid singularities and to reduce the number of DH parameters. Kinematic and dynamic of finger motions are evaluated using an experimental setup with mechanical parts produced by 3D printing and different actuators. Finally, experimental results are compared with the theoretical values and demonstrate the accuracy of our model.
... A hybrid method for the optimum design of a 2R spatial manipulator using prescribed end-effector poses is presented in paper (Sagris et al., 2004a). A combination of the exact synthesis techniques with optimization methods is used in (Perez and McCarthy, 2000) to design a spatial RR chain for an arbitrary end-effector trajectory, as well as in (Perez and McCarthy, 2005) where the method is extended in the geometric design of 3-DOF serial manipulators (RRP,RPR, and PRR). ...
In the present paper an optimization algorithm to find out the geometric design parameters of an open loop spatial robot with three revolute joints is described. The design variables include the base position, the geometry of the links and the joint angles of the robot and are calculated so that the manipulator will be able to place its end-effector at prescribed poses, avoiding simultaneously singular configurations. The developed algorithm uses the Denavit-Hartenberg parameters and 4x4 homogeneous matrices to obtain the kinematic equations of the robot. The optimization problem is solved with a hybrid method that combines a genetic algorithm, a quasi-Newton algorithm and a constraints handling method. To examine the efficiency of the method, numerical examples for one, three and five prescribed poses of the end-effector are applied.
... This involves equating the kinematics equations of the chain to four selected positions and solving for the Denavit -Hartenberg parameters that satisfy these matrix equations. Perez and McCarthy [7,8] formulate and solve the design equations for the RPC and RRP and related chains. This work builds on a tradition of spatial mechanism synthesis dating back to Suh [9] and Tsai and Roth [10] (see also references [11][12][13]). ...
... The difference between this equation and equation (8) is that the coordinates of the joint axes of the serial chain are defined in the world frame. ...
This article presents a formulation of the design equations for a spatial serial chain that uses the Clifford algebra exponential form of its kinematics equations. This is the even Clifford algebra C+(P3), known as dual quaternions. These equations define the position and orientation of the end effector in terms of rotations or translations about or along the joint axes of the chain. Because the coordinates of these axes appear explicitly, specifying a set of task positions these equations can be solved to determine the location of the joints. At the same time, joint parameters or certain dimensions are specified to ensure that the resulting robotic system has specific features.
... This involves equating the kinematics equations of the chain to four selected positions and solving for the Denavit-Hartenberg parameters that satisfy these matrix equations. Perez and McCarthy [11] formulate and solve the design equations for the RRP and related chains. This work builds on a tradition of spatial mechanism synthesis dating back to Suh [9], and Tsai and Roth [10]-also see Suh and Radcliffe [12], and more recently McCarthy [13]. ...
... Using this notation the Clifford algebra product of ele-ments =â + A andB =b + B takes the form C = (b+B)(â+A) = (bâ−B·A)+(âB+bA+B×A), (11) where the usual vector dot and cross products are extended linearly to dual vectors. ...
In this paper we formulate the “generalized inverse kinematics problem” for a spatial serial chain, where the goal is to determine values for structural parameters as well as for the joint parameters. The kinematics equations of the chain are formulated first using matrix exponentials and then cast into a form based on exponentials in a Clifford algebra. These equations contain the coordinates of the joint axes explicitly and have a systematic structure that can be exploited in their solution. As an example we fit a seven degree-of-freedom CCS chain to a 12 position task trajectory. In this problem, we can also specify desired values for the first two joint angles, and compute the structural parameters and the remaining joint angles.
This paper proposes a novel synthesis method of constructing plane-space switching mechanisms based on the symmetric plane of the regular prism. First, the structure equation and motion characteristic of plane-symmetric eight-bar linkage are presented. Then the plane-symmetric seven-bar linkage and rhombic Bricard linkage are obtained by locking the joint of eight-bar linkage. Four types of plane-space switching mechanisms are constructed based on the synthesis method and switching linkage units. These switching mechanisms can expand completely into planar configurations and fold completely into spatial configurations. Subsequently, the kinematics of the coupled branch chain is analyzed, through which the folded and contractive characteristics of the mechanism are revealed. Then the concept of distributed circle of joints is proposed, and the enveloping performance of the mechanism is approximately analyzed. This paper provides a new idea and synthesis method for designing new deployable mechanisms.
In this paper, we propose an optimization method to determine the design parameters comprising joint displacement parameters in a serial manipulator having small degrees of freedom realizing an approximated target trajectory. Using generalized differential kinematics, we can achieve efficient optimization without solving the inner-loop optimization required to obtain the reachable points.
To overcome the drawback of small displacement, large pressure fluctuation and unbalanced radial force of a rotary positive displacement pump, the rotating-guide-bar and gear mechanisms assembled driving systems of differential velocity vane pump with the cranks and the guide-bars as active parts are presented in this paper. With variation of the motion characteristic coefficient on the rotating-guide-bar and gear mechanisms assembled driving systems, their motion characteristics and laws are investigated. The basic parameter equations are established and the kinematics characteristics and mechanics performance are analyzed for these two types of driving systems. The results show that the transmission performance of rotating-guide-bar and gear mechanisms assembled driving system with the guide-bars as active parts is superior to that with cranks as active parts.
